The generator matrix

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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+43x^80+260x^81+587x^82+894x^83+1259x^84+1550x^85+1655x^86+1928x^87+2086x^88+2224x^89+2599x^90+2580x^91+2540x^92+2562x^93+2270x^94+1964x^95+1727x^96+1292x^97+872x^98+692x^99+431x^100+262x^101+182x^102+106x^103+97x^104+40x^105+26x^106+26x^107+5x^108+2x^109+1x^110+2x^111+2x^112+1x^116

The gray image is a linear code over GF(2) with n=364, k=15 and d=160.
This code was found by Heurico 1.16 in 63.1 seconds.