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

generates a code of length 94 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+42x^81+131x^82+196x^83+270x^84+374x^85+424x^86+578x^87+632x^88+788x^89+908x^90+988x^91+1148x^92+1146x^93+1284x^94+1164x^95+1158x^96+1076x^97+845x^98+780x^99+578x^100+472x^101+350x^102+252x^103+228x^104+162x^105+118x^106+102x^107+66x^108+32x^109+30x^110+30x^111+13x^112+4x^113+5x^114+6x^115+2x^116+1x^130

The gray image is a linear code over GF(2) with n=376, k=14 and d=162.
This code was found by Heurico 1.16 in 35.2 seconds.