The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 X 1 1 1 1 X X 1 1 X 1 1 1 1 X 1 1 1 1 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X 2X 2X X X X 0 X X X 2X 0 0 2X X X 2X 0 2X 0 X X X 2X 0 0 X X 2X 0 X 0 0 0 2X X X 2X 0 2X X 0 0 2X X 0 X X X 2X X X 2X 0 X X X X X X 0 X 2X X 2X 2X 0 0 2X 2X 2X 2X
0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X 2X 0 X X 2X 2X 2X 2X 2X 2X X 2X 0 X 2X 0 2X 0 X X 0 2X 0 X X X X 0 2X 0 0 X X X 0 X 2X 0 X 2X 0 X 2X 2X X 2X X 0 2X X X 0 2X 2X X 0 2X X 0 0 X X 0 0 2X 0 0 X X X 2X
0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 0 X X 0 2X X 0 0 0 X X X 2X 2X 2X 0 X 0 0 2X 2X 0 2X X X 0 X 0 X 2X 0 0 X X 2X X 2X 2X 0 X X 0 X X X X 2X 2X 2X 2X 0 2X 2X 2X 0 0 2X 2X 0 0 X 2X 2X 0 2X 0 X 0 0 0 2X
0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X 2X X 0 0 0 X 0 0 2X X X X 0 0 2X 0 2X 2X 2X 0 2X X X 2X 0 X 2X X X 2X 2X X X 0 X 2X 0 2X 0 X 0 X 0 2X 2X X 0 0 0 X X 2X 0 X X 2X 2X 2X X 2X 0 X 2X 0 0 2X X 2X 2X X X
0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 0 2X X X 2X 2X X 0 0 2X 2X 2X 2X 0 0 2X X 0 2X 0 2X X 2X 0 X X X 2X X 2X 2X 0 0 2X 0 2X 0 2X X 0 X 2X X X 2X X 2X X 0 2X 0 X 0 0 2X 2X X 0 2X 0 X X 0 X 2X 0 X X 2X 0 0
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X X X X X 2X 0 0 X 2X 0 X 2X 2X X X 2X 2X 0 X 2X X 0 X 0 X 2X X X X X 0 X 2X 2X 2X X 0 2X 2X 2X 2X 2X X 0 2X 2X 2X 0 2X 0 X 0 X 2X X 0 0 2X X 0 0 X 0 X 0 2X 2X 0 X 2X
generates a code of length 93 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.
Homogenous weight enumerator: w(x)=1x^0+126x^168+180x^171+224x^174+18x^175+232x^177+162x^178+202x^180+594x^181+194x^183+1152x^184+164x^186+1296x^187+132x^189+864x^190+142x^192+288x^193+124x^195+102x^198+82x^201+58x^204+76x^207+46x^210+38x^213+34x^216+14x^219+12x^222+2x^225+2x^258
The gray image is a linear code over GF(3) with n=279, k=8 and d=168.
This code was found by Heurico 1.16 in 3.22 seconds.