The generator matrix

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

generates a code of length 40 over Z4 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+50x^32+74x^33+109x^34+160x^35+138x^36+140x^37+157x^38+136x^39+157x^40+160x^41+141x^42+152x^43+109x^44+116x^45+77x^46+56x^47+50x^48+22x^49+26x^50+8x^51+5x^52+2x^54+2x^56

The gray image is a code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.10 in 0.109 seconds.