The generator matrix

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

generates a code of length 80 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+163x^72+308x^74+340x^76+262x^78+201x^80+166x^82+195x^84+112x^86+97x^88+72x^90+54x^92+34x^94+34x^96+6x^98+3x^100

The gray image is a code over GF(2) with n=160, k=11 and d=72.
This code was found by Heurico 1.10 in 1.36 seconds.