The generator matrix

1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 X 0 X 1 1 1 1 1 0 1 1 0 1 1 1 1 0 X 0 X 0 1 1 1 0 1 1 0 X X X 0 0 0 X 1 X 1 1 1 0 1 X 1 X 1 1 1 X 1 X 0 1 0 1 0 0 X X X 1 1 1 1 0 1 0
0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X X+1 X 1 1 1 0 1 X+1 X+1 0 X+1 X+1 1 1 X X X+1 1 1 1 1 1 X X+1 1 1 1 X 0 1 0 1 0 0 0 1 X X 1 0 X+1 X 1 X 1 X X+1 X 1 X 0 1 1 1 1 X+1 1 1 1 1 1 1 X+1 X+1 X X X+1 0
0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 1 1 1 1 X 1 X+1 0 X X 1 0 1 1 0 X+1 1 X+1 0 X+1 X 0 1 X 1 0 0 X X+1 X 0 1 1 1 X 1 X 1 1 1 X+1 1 1 X 0 0 X 0 X+1 1 1 X+1 0 1 X+1 X+1 X 1 0 1 0 X+1 X 1 0 0 1 X+1 0
0 0 0 1 0 0 0 1 1 1 1 1 0 1 X X+1 0 1 X 0 X 1 X 1 X+1 X 0 X+1 X+1 X+1 X X X+1 0 0 1 X 1 0 X X 1 X 0 1 X 1 X+1 0 1 X 1 X+1 X X+1 1 X 1 X 0 X+1 X 1 X X+1 X+1 X+1 X 1 1 1 X+1 0 0 0 0 X+1 1 0 X+1 0 0 X+1 1
0 0 0 0 1 0 1 0 X+1 1 1 1 X X+1 1 X 1 X X+1 1 0 X+1 X+1 0 X+1 X+1 X 0 X 1 0 1 X+1 0 X X X+1 X X+1 X+1 X+1 X+1 X+1 1 X+1 1 0 1 X+1 X+1 0 X X+1 X+1 X 1 X+1 1 0 1 0 1 X X 1 X+1 1 1 X+1 0 X+1 1 1 0 X+1 0 1 X 0 X+1 1 X+1 0 X
0 0 0 0 0 1 1 X+1 X 1 0 X 1 X+1 X 0 X+1 X+1 0 X+1 0 1 X 0 1 X+1 X+1 X+1 X X+1 X+1 X 0 0 X+1 1 1 0 0 X X+1 1 1 1 0 0 0 0 X 0 X+1 0 X X X X+1 1 1 1 1 X X+1 X+1 1 0 0 X+1 X X+1 1 0 X+1 1 X 1 X X 1 X X+1 0 1 X X+1
0 0 0 0 0 0 X X 0 0 0 0 0 0 X X X 0 0 0 X X X X X 0 X 0 X 0 X 0 0 X X X X X 0 0 0 0 X 0 X 0 X X X 0 X X X 0 0 X X X 0 X 0 0 0 0 0 0 0 X X X X X X 0 0 0 0 0 0 X X 0 X X

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+155x^72+494x^74+640x^76+726x^78+962x^80+794x^82+828x^84+868x^86+766x^88+712x^90+534x^92+328x^94+213x^96+96x^98+52x^100+14x^102+7x^104+2x^108

The gray image is a linear code over GF(2) with n=168, k=13 and d=72.
This code was found by Heurico 1.10 in 4.2 seconds.