The generator matrix

 1  0  0  0  0  0  1  1  1  2  1  2  1  1  2  0  1  1  1  1  2  1  2  1  2  1  2  0  1  2  1  2  0  1  0  1  1  1  2  2  2  1  1  1  2  0  2  2  2  2  1  1  1  0  1  0  2  1  2  0  1  0  1  1  1  0  1  0  0  0  1  1  1  1  2  0  1  2  0  2  2  0
 0  1  0  0  0  0  2  2  2  0  2  0  0  2  2  2  2  2  2  2  2  0  2  2  2  2  0  2  0  2  0  0  2  2  2  0  3  3  1  1  1  3  1  1  1  1  1  1  1  1  3  1  1  1  1  1  1  3  1  1  3  1  2  2  2  2  0  1  2  1  1  1  2  3  1  1  2  1  0  1  0  2
 0  0  1  0  0  0  0  0  0  2  0  0  0  2  2  2  2  3  3  3  1  3  1  1  1  1  1  1  3  1  1  1  2  1  1  0  0  2  2  3  1  1  1  3  0  0  2  1  0  1  2  2  3  3  1  0  1  0  3  1  2  3  3  1  3  1  1  0  1  0  3  1  2  0  3  1  1  2  1  3  2  1
 0  0  0  1  0  0  0  0  2  2  3  1  3  1  1  1  1  0  2  3  0  1  1  0  3  3  1  1  0  0  3  2  0  2  0  2  1  1  2  1  2  0  0  1  1  2  1  1  3  3  3  2  0  0  1  3  0  2  0  1  0  2  2  1  1  2  0  1  2  1  0  1  2  1  3  0  2  0  3  1  1  3
 0  0  0  0  1  0  0  3  3  1  1  1  3  2  0  1  0  1  2  3  2  0  3  1  0  1  2  3  2  1  2  3  1  1  0  0  2  3  3  2  0  0  2  2  3  2  3  1  1  3  3  1  1  3  0  2  0  2  3  3  0  0  3  0  0  0  2  0  1  3  3  1  1  1  2  1  3  2  1  3  1  3
 0  0  0  0  0  1  1  3  2  1  0  3  3  0  1  2  3  2  3  1  3  2  0  3  0  2  1  3  2  0  3  1  0  3  1  3  3  2  0  3  2  1  2  1  3  3  2  2  3  1  1  1  3  3  1  0  3  2  1  2  3  3  0  2  2  3  3  1  2  2  2  3  3  0  2  0  1  1  2  0  3  0

generates a code of length 82 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+200x^72+384x^74+489x^76+420x^78+455x^80+418x^82+432x^84+342x^86+344x^88+224x^90+189x^92+100x^94+54x^96+30x^98+10x^100+2x^102+2x^104

The gray image is a code over GF(2) with n=164, k=12 and d=72.
This code was found by Heurico 1.16 in 3.1 seconds.