The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+202x^32+400x^34+567x^36+578x^38+605x^40+642x^42+525x^44+344x^46+166x^48+50x^50+12x^52+2x^54+2x^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 1.19 seconds.