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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+50x^77+94x^78+60x^79+102x^80+112x^81+172x^82+198x^83+185x^84+234x^85+166x^86+162x^87+112x^88+92x^89+94x^90+62x^91+38x^92+18x^93+26x^94+26x^95+9x^96+4x^97+21x^98+4x^99+1x^100+2x^101+2x^102+1x^146

The gray image is a linear code over GF(2) with n=340, k=11 and d=154.
This code was found by Heurico 1.16 in 1.18 seconds.