The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+315x^32+184x^34+694x^36+330x^38+1036x^40+336x^42+756x^44+164x^46+240x^48+8x^50+22x^52+2x^54+8x^56

The gray image is a code over GF(2) with n=80, k=12 and d=32.
This code was found by Heurico 1.16 in 38.4 seconds.