The generator matrix

 1  0  0  1  1  1  0  1  X X^2  1  1 X^2+X  1  1 X^2  1  X  0  1  1  X  1  X  1  1  X  1  1  1  X  0  1  1  1  1  1  X  0  1 X^2+X X^2+X X^2+X X^2+X  1 X^2  1  X  0  0  1  1  1 X^2  1  1  1  X  1  1  1  1 X^2  1 X^2 X^2+X  1 X^2 X^2+X  1 X^2+X X^2  1  1  1 X^2+X  1  0 X^2+X  1 X^2 X^2  1 X^2+X  1  1  1  0  0 X^2 X^2 X^2 X^2+X  0
 0  1  0  0  1  1  1  X  1 X^2+X X^2+X X^2+1  1 X+1 X^2  1 X^2+X+1  0  1 X+1 X^2 X^2+X X^2+X  1 X^2+X+1  X  1  1 X^2+1  1  1  1 X^2+X  0 X^2+1 X^2+X  X  1  1 X^2+X+1  1  0  1  1 X+1  1 X+1  X  0 X^2+X  0 X^2+X+1 X^2+X X^2 X^2+1  0  0  1 X^2 X+1 X^2 X^2+X+1  1 X^2  1  0 X^2  1 X^2+X  X  X  1  1  X X^2+X  1  1  X  1 X^2+1  1 X^2 X^2+X  1 X+1 X^2+X+1 X+1  1  1  X  X X^2  0  1
 0  0  1 X+1 X^2+X+1  0 X+1  1 X^2  1  0  1  1  0 X^2+1  X  1  1 X^2+1  X X^2+X  1 X^2+X+1 X^2+X+1 X^2+X+1  X X^2+X X^2+X  X  1 X^2+X X+1 X+1  X  0  1 X^2  0 X^2+1 X^2+X+1 X^2+1  1 X^2  X  1 X^2+1 X^2  1  1  1  0 X^2+X  X  1  1 X+1 X^2+X X^2+X+1 X^2+X X^2  1 X^2+X+1  0  1  0  1 X+1  1  1 X+1  1 X^2 X+1 X+1 X^2+X+1 X^2 X^2+1  1  1  X  1  1  0  X X^2+X+1 X^2+1  X X^2+X+1  0  1  1  1  1 X^2+X
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2
 0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0

generates a code of length 94 over Z2[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+80x^87+257x^88+360x^89+379x^90+344x^91+351x^92+384x^93+310x^94+268x^95+251x^96+242x^97+215x^98+116x^99+96x^100+126x^101+78x^102+72x^103+55x^104+38x^105+35x^106+12x^107+9x^108+2x^109+4x^110+4x^111+4x^112+3x^114

The gray image is a linear code over GF(2) with n=376, k=12 and d=174.
This code was found by Heurico 1.16 in 1.53 seconds.