The generator matrix

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

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+156x^72+52x^73+262x^74+340x^75+363x^76+888x^77+444x^78+1552x^79+425x^80+2240x^81+478x^82+2384x^83+439x^84+1960x^85+436x^86+1512x^87+356x^88+908x^89+270x^90+348x^91+207x^92+96x^93+128x^94+8x^95+61x^96+30x^98+29x^100+8x^104+2x^108+1x^112

The gray image is a linear code over GF(2) with n=332, k=14 and d=144.
This code was found by Heurico 1.16 in 21.4 seconds.