The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+76x^79+114x^80+260x^81+234x^82+410x^83+254x^84+432x^85+226x^86+368x^87+187x^88+356x^89+208x^90+304x^91+164x^92+188x^93+65x^94+100x^95+35x^96+28x^97+23x^98+14x^99+9x^100+12x^101+9x^102+8x^103+2x^104+4x^105+3x^106+1x^108+1x^112

The gray image is a linear code over GF(2) with n=348, k=12 and d=158.
This code was found by Heurico 1.16 in 1.67 seconds.