The generator matrix

 1  0  0  0  1  1  1  X  1  1 X^2+X  1  1  X X^2 X^2  1  1  1  X  X  1  1 X^2 X^2+X  1  0  1 X^2+X  1  X  1  1  1  1  1  X X^2  1  X X^2+X  1  1 X^2+X  1  1 X^2  1  1  X  1 X^2+X X^2+X  1 X^2  1  1  X  1  1  X  1  1  1 X^2+X X^2  1  1  1 X^2+X  X  1  1  1 X^2+X  X  1  1  0  1  X  X  0  1 X^2+X  1 X^2 X^2+X  1  0 X^2+X  1  1  1
 0  1  0  0  X  1 X^2+X+1  1 X+1 X^2  1  X X^2+1  1  0  1  0  X X+1  0  1 X^2+1  0  1  1 X^2+1 X^2  X  X X+1  1  X X^2+1 X^2 X^2+X X^2+X X^2+X  1 X^2+1  1 X^2 X+1 X^2+X+1  1 X+1 X^2+1 X^2  0  0  1 X^2  1  X  X  X  1 X^2  1  X X^2+X+1 X^2+X X^2+X+1  X X^2+X+1  1  X X^2  0 X+1  0  1 X+1 X+1 X^2+1  0  1 X^2+X X^2+X+1 X^2 X^2+X  1  X  1 X^2  1 X^2+X+1  1  1 X^2+X  1  0  1 X^2  0
 0  0  1  0  0  0  0 X^2 X^2+1 X^2+1  1  1 X^2+X+1 X^2+X+1  1  X  X X+1 X+1 X^2  1  X X^2+X X^2+X+1  0  X  1 X^2+X+1  1 X^2+1 X+1 X^2  0 X+1  0  1  1 X^2+X+1 X^2+1 X^2+X  1  1 X^2+X X^2+X X^2+X  X X^2+X X^2+1 X^2 X^2  1 X+1  1  0  1 X^2+X  1 X^2+1 X^2+X  0  1 X^2 X^2 X^2+1  0  X X^2+X  1 X^2+1  1 X^2+X  1 X^2+X+1  0  X X^2+X+1 X^2+X+1  1  0  1  X  1 X^2+X X^2  X X+1 X^2+1  0 X+1 X^2+1  1 X+1 X^2  0
 0  0  0  1  1 X^2+X+1 X^2+X X^2+1 X+1  1 X^2  0  X X+1 X^2+X+1  0 X+1  1  X  1 X^2+X X^2+X+1 X^2+X X^2+1 X+1  X X^2+X  0 X^2+X+1 X^2+X+1 X+1 X^2+X  1 X^2+1 X+1 X^2+X  X X^2+X X^2+X X+1 X^2+1 X^2+1  X X^2+X  1  0  1 X^2+X+1  1 X^2+X+1  X X^2+X X^2  X X+1  1  0  1  X X^2+X X^2+1  X  0  X  0  1  0  0 X^2  1  0  1 X^2+X X^2  1  0  1 X^2  1 X^2+X+1 X^2+1 X^2+X X^2+1 X^2+X  X X+1  X X^2+X+1  X  X X^2+X+1 X^2+1 X^2+X+1  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  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 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  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 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  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 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 83.

Homogenous weight enumerator: w(x)=1x^0+66x^83+262x^84+648x^85+879x^86+1236x^87+1357x^88+1950x^89+1932x^90+2244x^91+2264x^92+2596x^93+2250x^94+2638x^95+2139x^96+2382x^97+1843x^98+1780x^99+1248x^100+1080x^101+715x^102+512x^103+297x^104+146x^105+108x^106+84x^107+40x^108+28x^109+11x^110+14x^111+6x^112+2x^113+5x^114+2x^115+2x^116+1x^126

The gray image is a linear code over GF(2) with n=376, k=15 and d=166.
This code was found by Heurico 1.16 in 67.8 seconds.