The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1  1  0 X^2+X  1  1  1  1 X^2+X X^2  1  1  1  0  1  1  0  1  1 X^2+X  1  1  X  1  1 X^2+X  0  1  1 X^2+X  0  1  X  1  1 X^2+X X^2  1 X^2  1  1  1  1  1 X^2+X  1  X  1  1  1  1  X  X  0  1 X^2+X X^2+X  1  0  1  1 X^2  X  X  1  1  0  1  X  0
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X X^2+1  1  0 X+1  1  1 X^2 X^2+1 X^2+X+1 X^2+X  1  1 X^2+X X^2+X+1 X^2+X  1  1 X^2+1  1 X^2+X+1  0  1  X X^2+1  1 X+1 X^2+X  1  1 X^2 X^2+X  1  1  X  1 X^2+X+1  0  1  1 X^2+X+1  1  1 X^2+X+1 X^2+1 X^2+X X^2  1 X^2+1  1  0  X X^2+1 X^2+X X^2+X  1  1 X^2+1  1  1 X^2+X+1  1 X^2+1 X^2+X+1  X X^2 X^2+X  1 X^2  1 X+1  X  1
 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^2+X  X X^2  X  X X^2 X^2+X X^2 X^2  0  X X^2+X X^2+X  0 X^2+X  0 X^2 X^2+X  0 X^2+X  X  X X^2  0  X  0  0  X  X  X X^2+X  0 X^2+X  0  X X^2 X^2+X X^2  0  X X^2+X X^2  0 X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2  X X^2+X  X  0 X^2+X X^2 X^2+X  X  X X^2+X X^2+X X^2 X^2+X  0 X^2  X  0
 0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 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  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0
 0  0  0  0  0  0  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 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+49x^72+74x^73+157x^74+268x^75+326x^76+644x^77+398x^78+762x^79+426x^80+844x^81+439x^82+918x^83+458x^84+684x^85+359x^86+514x^87+204x^88+268x^89+121x^90+86x^91+48x^92+38x^93+47x^94+12x^95+15x^96+6x^97+11x^98+8x^100+2x^101+3x^102+1x^104+1x^110

The gray image is a linear code over GF(2) with n=328, k=13 and d=144.
This code was found by Heurico 1.16 in 5.61 seconds.