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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+48x^72+112x^73+150x^74+228x^75+287x^76+330x^77+398x^78+456x^79+547x^80+642x^81+672x^82+698x^83+671x^84+598x^85+506x^86+418x^87+345x^88+240x^89+204x^90+178x^91+130x^92+90x^93+66x^94+62x^95+41x^96+30x^97+18x^98+8x^99+8x^100+6x^101+2x^102+1x^104+1x^120

The gray image is a linear code over GF(2) with n=332, k=13 and d=144.
This code was found by Heurico 1.16 in 8.12 seconds.