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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+108x^72+8x^73+278x^74+44x^75+402x^76+128x^77+340x^78+244x^79+497x^80+216x^81+478x^82+180x^83+340x^84+144x^85+210x^86+44x^87+181x^88+16x^89+102x^90+54x^92+48x^94+12x^96+14x^98+4x^100+2x^102+1x^120

The gray image is a linear code over GF(2) with n=324, k=12 and d=144.
This code was found by Heurico 1.16 in 1.9 seconds.