The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1 X^2  1 X^2+X  1  0  1  1 X^2 X^2  1 X^2+X  1 X^2+X  1 X^2  1  1  1  1  1  1 X^2+X  1 X^2 X^2+X X^2  X  1 X^2+X  X  1  0  1  1  1 X^2+X X^2+X X^2  1  1  0 X^2 X^2+X  1  1 X^2  1 X^2+X  X  1  1  X  1  X  1  1 X^2  1 X^2+X  X  X  1  1  1  1  0  1  0  1  1  1  1 X^2+X  1  1  1  1
 0  1  0  0  0  0  0 X^2 X^2  1  1  1  1  1  1 X+1 X^2+X X^2+X X^2+X  1  1 X^2+X+1 X^2+X X+1  1 X+1  0 X^2+X X+1 X^2+1  X  0 X+1  1 X+1  0  0  1  1 X^2 X^2  1  X  1  X  1 X^2+1 X^2+X  1 X^2+X  X  1  1  1  X  1  0 X^2+X X^2 X^2+X X^2 X^2+X+1 X^2 X^2+X  1  1 X^2  0  1 X^2 X^2  1  1 X^2+X+1  0 X^2+1  1  0  X  1 X^2+1  X X+1  0  1  X X^2+X X^2+X+1  0
 0  0  1  0  0 X^2  1 X^2+1  1  0  1 X+1 X^2+X+1 X^2+1  0  X  1 X^2+X X^2+X+1 X^2+X  0 X^2+X X^2  1 X^2+1 X^2+1  1 X^2+1  0  X  X X^2  1  0 X+1  1  1 X+1 X^2+1  1  0 X^2+1  1 X^2+X+1 X^2  0  X  X  1  1 X^2+X+1  X  X X^2  X X+1  X  0 X^2  1  1 X+1  X X^2  0 X+1 X^2+X+1 X^2+X X^2 X^2+X X^2+X  X  X  0 X+1  0 X^2+X+1  1 X^2+X+1 X^2+X X^2 X^2+X X^2+X X^2+1 X+1 X^2+1 X+1  0 X^2+X
 0  0  0  1  0 X^2+1  1  0  1 X^2 X^2+1 X+1 X^2 X^2+X X^2+1 X^2+X+1 X^2+X  0 X^2+X X+1 X^2+X X^2+X  1 X^2+X  1 X+1 X+1 X^2+X+1 X^2+1 X^2+X  1 X^2+X  X X+1  X  X X^2+1  1  0  X  X  X X^2+X  X X^2+1 X^2+X  1  1 X^2+X+1 X^2+X+1  1 X^2+X  X X+1  1 X^2+1 X^2+1  1 X^2+X+1  0 X^2+X X^2 X^2+X+1  1  X  X X^2+1 X^2 X^2+X  0  X X+1  1  X  0 X^2+X+1  1 X^2+X  1 X^2 X^2+X X^2+X X^2+X+1 X^2+X+1 X^2+X  X  X  1 X^2+X
 0  0  0  0  1  1 X^2  1  1 X^2+1 X^2  1 X+1  0  1  0 X^2+1 X^2+X+1  X  X X^2+X+1 X^2+X X^2+X+1  1 X+1  X X^2+X X^2+1 X^2+X+1 X^2+1  X X^2+X+1 X+1 X+1  X X^2+X+1 X^2+1 X^2+1 X+1  1  1 X^2  X X^2  X X^2 X^2 X+1  X X^2 X+1 X^2+X X^2+X+1 X^2+X  1 X+1  0 X^2+1 X^2+1 X^2  1 X^2 X^2+X+1 X^2 X^2+1 X^2+1 X^2+X X^2 X^2+1  X  1  X X+1 X+1 X^2+1 X+1  X X^2+X  1 X^2  X X^2 X+1 X^2  0  0  1 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+214x^79+544x^80+872x^81+1340x^82+1282x^83+1917x^84+1894x^85+2375x^86+2390x^87+2639x^88+2388x^89+2585x^90+2162x^91+2415x^92+1752x^93+1785x^94+1274x^95+1004x^96+748x^97+567x^98+242x^99+166x^100+114x^101+48x^102+18x^103+12x^104+8x^105+4x^106+2x^107+4x^108+2x^116

The gray image is a linear code over GF(2) with n=356, k=15 and d=158.
This code was found by Heurico 1.13 in 19.5 seconds.