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

generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+42x^80+106x^82+12x^83+161x^84+44x^85+207x^86+144x^87+225x^88+336x^89+214x^90+488x^91+202x^92+488x^93+204x^94+336x^95+204x^96+144x^97+182x^98+44x^99+134x^100+12x^101+96x^102+28x^104+6x^106+11x^108+4x^110+10x^112+4x^114+3x^116+1x^118+1x^120+1x^124+1x^144

The gray image is a linear code over GF(2) with n=368, k=12 and d=160.
This code was found by Heurico 1.16 in 2.72 seconds.