The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  2  1  1  1  2  1  2  1  1  1  1  1  2  1  1  1  1  2  1  2  2  2  1  1  2  1  1  2  2  1  0  1  1  1  2  2  2
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  2  2  0  0  2  0  0  2  2  0  2  2  2  2  0  0  0  0  0  2  2  0  2  2  2  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  0  0  2  2  2  0  0  2  2  2  2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  2  0  0  2  0  2  0  2  2  2  0  0  0  0  0  0  2  2  0  2  0  0  2  0  2  0  0  2  2  2  0  2  0  2  2  0  2  2  0  0  2  0  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  0  0  2  2  2  2  2  2  0  2  0  2  2  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  2  0  2  0  0  2  0  2  0  0  0  0  0  2  2  0  0  2  0  0  0  2  0  0  2  2  2  2  2  2  0  2  2  2  0  0  2  2  0  0  0  0  2  2  0  0  0  2  2  2  0  2  0  0  0  2  2  2  0  0  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  0  0  2  0  0  0  2  2  0  2  2  0  2  2  2  2  0  2  0  0  2  2  0  2  0  2  0  2  0  0  2  0  2  0  0  2  2  2  0  2  2  0  0  0  2  0  2  0  2  0  2  0  2  2  0  2  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  0  2  0  0  2  2  0  2  2  2  0  2  2  2  0  0  0  0  2  2  0  2  0  2  0  0  2  0  2  2  2  2  2  0  0  2  0  0  0  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  0  0  2  0  2  2  2  0  2  0  2  2  2  0  2  2  0  2  0  0  2  0  2  2  0  0  2  0  2  0  2  2  2  2  0  0  2  2  2  0  0  0  0  0  0  0  0  2  0  2  2  2  0  2  2  2  0  0  2  0  0  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  0  0  2  0  0  2  2  2  0  0  2  2  0  2  0  2  0  0  2  0  0  2  2  0  2  0  0  2  0  2  0  0  2  0  2  0  2  2  2  0  0  0  2  2  0  0  2  0  2  0  2
 0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  2  2  0  2  2  2  2  0  2  0  2  2  2  0  2  0  2  0  2  0  0  2  2  0  2  0  0  0  2  0  0  2  2  2  2  0  0  2  0  2  0  0  2  0  2  2  2  2  2  2  2  0  2  0  0  2  2  0  0  2  0  0  0  2  0  2

generates a code of length 84 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+126x^72+4x^74+218x^76+76x^78+318x^80+184x^82+316x^84+168x^86+230x^88+68x^90+165x^92+12x^94+92x^96+49x^100+14x^104+3x^108+3x^112+1x^132

The gray image is a code over GF(2) with n=168, k=11 and d=72.
This code was found by Heurico 1.16 in 1.49 seconds.