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

generates a code of length 95 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+60x^82+136x^83+204x^84+298x^85+351x^86+446x^87+584x^88+642x^89+757x^90+914x^91+1032x^92+1120x^93+1160x^94+1174x^95+1129x^96+1130x^97+1093x^98+898x^99+745x^100+590x^101+447x^102+360x^103+271x^104+238x^105+159x^106+146x^107+98x^108+68x^109+55x^110+18x^111+28x^112+6x^113+11x^114+2x^115+1x^116+4x^117+2x^118+2x^119+3x^120+1x^126

The gray image is a linear code over GF(2) with n=380, k=14 and d=164.
This code was found by Heurico 1.16 in 35.7 seconds.