The generator matrix

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

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+146x^72+100x^74+379x^76+288x^78+531x^80+384x^82+518x^84+376x^86+529x^88+284x^90+291x^92+104x^94+76x^96+53x^100+25x^104+6x^108+4x^112+1x^116

The gray image is a linear code over GF(2) with n=168, k=12 and d=72.
This code was found by Heurico 1.16 in 4.55 seconds.