The generator matrix

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

generates a code of length 72 over Z4 who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+16x^73+6x^74+6x^76+2x^78+1x^80

The gray image is a code over GF(2) with n=144, k=5 and d=73.
This code was found by Heurico 1.16 in 0.0733 seconds.