The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+274x^79+624x^80+870x^81+1107x^82+1492x^83+1814x^84+1946x^85+2149x^86+2308x^87+2478x^88+2560x^89+2606x^90+2540x^91+2310x^92+1996x^93+1638x^94+1296x^95+971x^96+676x^97+437x^98+258x^99+166x^100+98x^101+57x^102+50x^103+16x^104+12x^105+6x^106+6x^107+2x^108+2x^112+2x^113

The gray image is a linear code over GF(2) with n=356, k=15 and d=158.
This code was found by Heurico 1.16 in 88.8 seconds.