The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+156x^73+212x^74+518x^75+423x^76+702x^77+454x^78+888x^79+539x^80+896x^81+498x^82+706x^83+370x^84+570x^85+275x^86+340x^87+165x^88+202x^89+75x^90+86x^91+26x^92+32x^93+19x^94+20x^95+11x^96+2x^97+3x^98+2x^99+1x^100

The gray image is a linear code over GF(2) with n=324, k=13 and d=146.
This code was found by Heurico 1.16 in 4.97 seconds.