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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+74x^69+167x^70+258x^71+298x^72+410x^73+462x^74+570x^75+778x^76+936x^77+1045x^78+1166x^79+1373x^80+1400x^81+1396x^82+1214x^83+1079x^84+972x^85+668x^86+536x^87+425x^88+276x^89+281x^90+152x^91+103x^92+138x^93+76x^94+64x^95+35x^96+18x^97+1x^98+8x^99+3x^100+1x^116

The gray image is a linear code over GF(2) with n=324, k=14 and d=138.
This code was found by Heurico 1.16 in 30 seconds.