The generator matrix

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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+84x^72+218x^74+180x^76+110x^78+129x^80+92x^82+56x^84+38x^86+32x^88+28x^90+24x^92+18x^94+6x^96+2x^98+6x^102

The gray image is a code over GF(2) with n=158, k=10 and d=72.
This code was found by Heurico 1.10 in 0.063 seconds.