The generator matrix

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

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+160x^72+76x^73+362x^74+224x^75+579x^76+424x^77+744x^78+528x^79+817x^80+576x^81+746x^82+528x^83+730x^84+408x^85+432x^86+240x^87+297x^88+52x^89+118x^90+16x^91+72x^92+24x^94+18x^96+6x^98+10x^100+3x^104+1x^108

The gray image is a linear code over GF(2) with n=324, k=13 and d=144.
This code was found by Heurico 1.16 in 5.8 seconds.