The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+29x^32+133x^34+135x^36+129x^38+160x^40+164x^42+153x^44+68x^46+24x^48+15x^50+7x^52+3x^54+2x^56+1x^60

The gray image is a code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0945 seconds.