The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^72+58x^73+41x^74+46x^75+51x^76+54x^77+47x^78+30x^79+18x^80+20x^81+17x^82+14x^83+10x^84+18x^85+11x^86+4x^87+4x^88+6x^89+6x^90+2x^92+4x^93+4x^94+2x^95+2x^96+1x^100+2x^110

The gray image is a code over GF(2) with n=156, k=9 and d=72.
This code was found by Heurico 1.16 in 0.13 seconds.