The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1 X^2+X  0  1  1 X^2+X  1  1  1 X^2  1  1  1 X^2  1  1  1 X^2+X  1 X^2+X  1  1  X  1  1  X  X  1  1  1  1  X  1 X^2+X  1 X^2  1  1 X^2+X  1 X^2  1 X^2+X  1  1 X^2+X  1 X^2  1  1  1  1  1 X^2  1  1  1  1  1  X  1 X^2  1  0  1  1  1  X
 0  1  1  0 X^2+X+1  1  X X+1  1  1  1  0 X^2+X+1 X^2+X  1  1  X X+1  1 X^2+1 X^2+X  0  1 X^2+1  1 X+1  1 X^2  1  X  1 X^2+X  1  X  X  1 X^2+1 X^2+X+1  1  1  X X+1  0 X^2+1  1 X^2+1  1  0  1 X+1 X+1  1  X  1 X^2+1  1 X^2+X  X  1  1  1 X+1  1 X^2+1 X^2+X+1 X^2+X  1  0  X X^2+1  0 X+1  1  X X^2  0  1 X^2+X+1  0 X^2+X  X
 0  0  X  0 X^2+X  0  0  0 X^2 X^2 X^2  X  0  X X^2+X X^2+X  X X^2+X  X  X  0  X  X  0  X X^2+X X^2  0 X^2  0  0  X X^2 X^2 X^2+X X^2+X  0  0  X  0  0 X^2 X^2+X  0  X X^2  X X^2  X  X  X X^2  0  X X^2 X^2 X^2+X  X X^2  X X^2+X  X X^2  0 X^2  X  X X^2+X  0  0 X^2 X^2+X  0  X  X X^2+X  X  X  X  0  0
 0  0  0  X  0  0  X X^2 X^2+X  X  X  X  X X^2+X X^2+X X^2+X X^2 X^2+X  0  X X^2 X^2 X^2  0  X  0  0  X X^2+X  X X^2+X  0 X^2 X^2+X  X X^2+X X^2  0 X^2  X X^2 X^2+X  X X^2+X X^2+X X^2 X^2+X  0  0  X X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2+X  0  0 X^2 X^2+X X^2+X X^2+X  0 X^2+X X^2  X X^2+X X^2 X^2+X X^2  0 X^2 X^2+X  X X^2 X^2+X X^2+X X^2+X  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  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  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 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+143x^72+80x^73+366x^74+248x^75+571x^76+356x^77+790x^78+520x^79+822x^80+620x^81+764x^82+560x^83+665x^84+412x^85+482x^86+200x^87+261x^88+68x^89+90x^90+8x^91+70x^92+54x^94+19x^96+12x^98+5x^100+2x^102+2x^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 5.62 seconds.