The generator matrix

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

generates a code of length 78 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+238x^72+84x^74+264x^76+52x^78+149x^80+32x^82+78x^84+20x^86+58x^88+4x^90+32x^92+10x^96+2x^108

The gray image is a code over GF(2) with n=156, k=10 and d=72.
This code was found by Heurico 1.16 in 52.7 seconds.