The generator matrix

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

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+178x^72+470x^73+1129x^74+1484x^75+2178x^76+2600x^77+3553x^78+3502x^79+4727x^80+4722x^81+5429x^82+5208x^83+5853x^84+4752x^85+5035x^86+3738x^87+3566x^88+2294x^89+1848x^90+1290x^91+900x^92+484x^93+290x^94+128x^95+88x^96+34x^97+26x^98+10x^99+9x^100+4x^101+2x^102+4x^104

The gray image is a linear code over GF(2) with n=332, k=16 and d=144.
This code was found by Heurico 1.13 in 69.3 seconds.