The generator matrix

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

generates a code of length 93 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+70x^82+268x^83+680x^84+780x^85+1424x^86+1388x^87+1909x^88+1804x^89+2388x^90+1908x^91+2842x^92+2132x^93+2760x^94+2034x^95+2474x^96+1764x^97+1900x^98+1136x^99+1089x^100+696x^101+544x^102+264x^103+222x^104+100x^105+82x^106+40x^107+21x^108+16x^109+12x^110+2x^111+10x^112+4x^113+4x^114

The gray image is a linear code over GF(2) with n=372, k=15 and d=164.
This code was found by Heurico 1.16 in 65.2 seconds.