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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+59x^76+133x^78+205x^80+64x^81+256x^82+128x^83+407x^84+192x^85+515x^86+256x^87+499x^88+192x^89+394x^90+128x^91+233x^92+64x^93+169x^94+98x^96+48x^98+15x^100+13x^102+13x^104+6x^106+3x^108+2x^110+2x^116+1x^140

The gray image is a linear code over GF(2) with n=348, k=12 and d=152.
This code was found by Heurico 1.16 in 2.48 seconds.