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 X^2+X  1  1  1 X^2+X  0 X^2  X  1  1  1 X^2+X X^2+X  X  X X^2+X  1 X^2+X  1 X^2+X  1 X^2+X  X  1  1  1  X  1  1  1  1  X  1  1  1 X^2 X^2+X  1  1 X^2+X  1  1  1  X X^2  0  1 X^2  1 X^2+X  1  1  1  1 X^2+X  X  1  X  1  0  1 X^2 X^2+X  0  X
 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 X^2+X  0 X+1 X^2+X  1  1  0  1 X^2  1 X^2+1 X^2  1  1 X^2+X  X X^2+X  1 X^2+X+1  1 X^2+1  0 X^2+X  1 X^2+X  0  1  0  0  X  1  1 X^2+X  1 X^2  1  1 X+1 X^2+X+1 X^2+X  0 X^2  X  0  X  1 X^2 X^2+X X+1  X  X  0  1 X^2+1  1  X  1 X^2+X X+1  1 X^2+1  X  1  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  1  X X+1  1  1 X^2  X  X  X  0  0  1 X^2+X+1 X+1  1 X^2+X  X  0 X+1 X^2 X^2+1  1  1 X^2+X+1 X+1 X+1 X^2+1 X+1  X X^2+X  X X^2 X^2+1 X^2+X  X X^2+X+1 X^2+1 X^2+1 X^2  1 X^2+1 X+1 X^2+X+1 X^2+X  X  X X+1  1 X+1  1 X^2 X^2 X^2+X X^2 X^2+X  1  0  X X^2+X X^2+X  1  1 X^2+X+1 X^2+X X^2+X
 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^2 X^2+X+1  1  0  X  1  1 X+1 X^2+X  1  1 X^2 X^2+X+1  X  1 X^2+X  0  0 X^2+1 X^2+1 X+1 X^2 X^2  1  X  X X^2+1 X+1 X^2 X^2+1 X^2+X+1 X^2+X  X  0  0  1  1  1 X+1  X X^2 X^2  1  1  0 X^2+X+1  1 X^2+1 X^2  0 X^2+X+1 X^2+1  X  X X^2 X+1  1  X X+1  X X^2+X X^2+1  1 X^2
 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 X^2 X^2+X X^2+X X^2 X^2  X  X X^2+X  0  X  X X^2 X^2+X X^2  0  X X^2+X X^2+X  0  0 X^2 X^2+X  X  0  X  X X^2  0  X X^2 X^2 X^2+X  X X^2 X^2+X X^2  X  0  0  0 X^2+X X^2+X  0  0  0 X^2  0  0 X^2+X  0 X^2  X X^2+X  X  0 X^2  0  X  0  0  X X^2+X X^2  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 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2  0  0  0 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+210x^75+483x^76+912x^77+1143x^78+1410x^79+1518x^80+2282x^81+2178x^82+2522x^83+2362x^84+2810x^85+2457x^86+2738x^87+2178x^88+2110x^89+1604x^90+1328x^91+827x^92+612x^93+387x^94+306x^95+163x^96+118x^97+30x^98+26x^99+20x^100+18x^101+9x^102+2x^103+2x^105+2x^107

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 58.8 seconds.