The generator matrix

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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+41x^74+106x^75+171x^76+274x^77+274x^78+314x^79+426x^80+462x^81+561x^82+620x^83+663x^84+668x^85+633x^86+596x^87+482x^88+430x^89+315x^90+258x^91+259x^92+146x^93+112x^94+114x^95+85x^96+50x^97+43x^98+40x^99+19x^100+16x^101+5x^102+5x^104+2x^105+1x^120

The gray image is a linear code over GF(2) with n=340, k=13 and d=148.
This code was found by Heurico 1.16 in 8.36 seconds.