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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+54x^74+156x^76+20x^77+212x^78+64x^79+338x^80+112x^81+399x^82+192x^83+413x^84+248x^85+410x^86+192x^87+384x^88+112x^89+309x^90+64x^91+175x^92+20x^93+124x^94+43x^96+10x^98+13x^100+14x^102+8x^104+3x^106+2x^108+2x^112+1x^114+1x^124

The gray image is a linear code over GF(2) with n=340, k=12 and d=148.
This code was found by Heurico 1.16 in 2.38 seconds.