The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  1  0  1  0  X  1  X  1  1  0  1  1  1  0  1  X  X  1  0  0  1  X  1  0  1  X  1  1  1  1  X  0  0  1  X  1  0  1  1  0  0  1  X  1  1  1  0  1  1  1  1  1  0  0  1  0  0  1  1  1  X  1  1  1  X  1  1  X  1  0  1
 0  1  0  0  1  1  1  0  0  1 X+1  1  1  X  0  X  0  1 X+1  1 X+1 X+1  1  X  0  1  1 X+1  1  X X+1  1  X  1  1  0  1  0  X  1  X X+1 X+1  1  1  X  X  1  1  1  X X+1  X  X  0  1 X+1  0  0  X  1  0  1  0 X+1  1  1  0  1  1  1  0  1  X  X X+1  X  X X+1  X  0  1  X  0
 0  0  1  1  1  0  1  0  1 X+1  0  X X+1  X  1  1  1  X X+1  1  0  0  0 X+1  X  1  0  X X+1  1 X+1  X  1  0  X  0  1  X  1  1  1  X  0 X+1 X+1  1 X+1  X  X  0  0 X+1  1  1  1  1  0  X  1  1  0  0 X+1  0  0  0 X+1 X+1  X  X X+1  0 X+1  1 X+1  0  0  1  1  0  1  1  0  0
 0  0  0  X  0  0  0  0  0  X  X  0  0  X  X  0  0  0  0  X  0  X  0  X  X  X  0  X  X  0  0  X  0  X  X  0  X  0  X  0  X  X  X  0  X  X  X  X  0  0  0  X  X  X  0  0  0  X  X  0  X  0  X  0  X  X  X  0  0  X  X  X  X  X  X  X  0  X  0  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  0  0  X  X  X  X  X  0  X  X  0  X  X  0  0  0  X  0  X  X  0  X  X  0  0  0  X  0  X  0  X  0  0  0  0  X  X  X  X  0  X  X  0  X  0  X  0  0  0  0  0  X  X  X  0  0  X  0  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  X  X  0  X  0  0  0  X  0  X  0  X  0  X  X  0  0  0  X  X  X  0  X  0  0  X  0  0  X  X  X  0  X  X  0  0  X  0  0  X  0  X  0  0  X  X  0  0  X  0  X  X  0  X  0  X  0  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  X  X  0  X  0  0  X  X  X  0  0  X  0  X  X  X  X  0  0  X  X  0  0  0  X  X  0  0  X  0  X  X  0  X  X  0  X  X  X  0  X  0  X  X  0  0  0  X  0  0  X  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  0  0  0  X  0  X  0  X  X  X  X  0  0  X  X  0  X  0  0  0  X  0  0  0  X  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  0  X  0  X  X  0  X  X  0  0  0  X  0  0  X  0  X  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0  0  0  X  X  0  X  0  0  0  X  X  0  X  X  X  0  X  0  X  X  0  X  X  X  0  0  0  0  0  X  0  X  X  X  X  X  X  X  X  0  0  X  0  0  0  X  0  0  X  0  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  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+57x^72+58x^73+102x^74+118x^75+190x^76+172x^77+183x^78+250x^79+247x^80+226x^81+223x^82+246x^83+196x^84+244x^85+188x^86+166x^87+146x^88+192x^89+169x^90+170x^91+107x^92+108x^93+100x^94+62x^95+58x^96+18x^97+41x^98+10x^99+18x^100+4x^101+8x^102+2x^103+3x^104+2x^105+9x^106+1x^108+1x^110

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 3.72 seconds.