The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^32+52x^33+128x^34+130x^35+144x^36+174x^37+139x^38+174x^39+141x^40+150x^41+138x^42+162x^43+126x^44+122x^45+80x^46+42x^47+43x^48+14x^49+22x^50+4x^51+10x^52+5x^54+1x^56

The gray image is a code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.16 in 0.309 seconds.