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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+44x^72+74x^73+108x^74+116x^75+156x^76+176x^77+218x^78+320x^79+347x^80+360x^81+395x^82+352x^83+315x^84+306x^85+183x^86+166x^87+106x^88+84x^89+74x^90+50x^91+38x^92+22x^93+28x^94+18x^95+14x^96+2x^97+14x^98+2x^99+3x^100+3x^102+1x^130

The gray image is a linear code over GF(2) with n=328, k=12 and d=144.
This code was found by Heurico 1.16 in 2.01 seconds.