The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  2  0  2  1  2  1  1  1  2  0  0  0  2  1  0  1  2  0  0  1  0  1  1  1  1  1  2  1
 0  1  0  0  0  1  1  1  2  0  3  1  1  1  1  3  2  3  0  2  1  1  1  1  0  3  1  1  2  0  0  0  2  3  1  2  0  0  0  2
 0  0  1  0  1  1  0  1  0  3  3  2  2  3  2  3  1  3  0  0  0  3  2  3  2  0  0  2  1  0  1  1  0  1  3  2  0  0  1  0
 0  0  0  1  1  0  1  1  1  0  1  2  3  0  1  3  0  0  2  3  2  1  1  1  1  2  2  3  2  1  1  2  1  0  0  3  2  2  3  1
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  0  2  2  0  0  0  0  2  2  2  2  2  0  0  2  2  0  0  0
 0  0  0  0  0  2  0  2  2  2  0  2  0  2  2  2  0  0  0  2  0  2  2  0  2  2  2  2  2  2  2  0  0  2  0  0  2  2  2  0
 0  0  0  0  0  0  2  2  2  2  0  2  0  2  2  0  0  2  2  0  2  0  0  0  0  0  2  0  0  2  0  2  2  2  2  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+39x^32+80x^33+110x^34+122x^35+156x^36+166x^37+135x^38+160x^39+156x^40+148x^41+164x^42+156x^43+112x^44+104x^45+78x^46+64x^47+44x^48+12x^49+22x^50+10x^51+4x^52+2x^53+3x^54

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 0.289 seconds.