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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+158x^75+490x^76+782x^77+1295x^78+1374x^79+1775x^80+1942x^81+2603x^82+2320x^83+2592x^84+2530x^85+2715x^86+2212x^87+2450x^88+1788x^89+1809x^90+1132x^91+1010x^92+722x^93+426x^94+270x^95+184x^96+104x^97+44x^98+18x^99+8x^100+2x^101+4x^102+4x^103+2x^104+2x^105

The gray image is a linear code over GF(2) with n=340, k=15 and d=150.
This code was found by Heurico 1.16 in 54.1 seconds.