The generator matrix

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

generates a code of length 72 over Z4 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+128x^62+356x^64+460x^66+521x^68+480x^70+496x^72+340x^74+414x^76+344x^78+249x^80+124x^82+121x^84+40x^86+18x^88+4x^90

The gray image is a code over GF(2) with n=144, k=12 and d=62.
This code was found by Heurico 1.10 in 0.938 seconds.