The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  2  1  1  2  1  2  1  1  2  1  1
 0  2  0  0  0  0  0  0  0  0  2  2  0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  2  2  2  0  2  0  0  2  2  0  0  0  0
 0  0  2  0  0  0  0  0  0  2  2  2  0  2  2  0  0  0  2  2  2  2  2  2  2  2  0  2  2  0  2  0  0  2  2  0  0  2  0  0
 0  0  0  2  0  0  0  0  0  2  0  2  2  2  0  2  0  2  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  2  0  0  0  0
 0  0  0  0  2  0  0  0  2  0  0  2  2  0  2  2  0  0  2  2  0  0  0  2  0  2  2  2  2  0  2  0  0  0  0  0  2  2  2  2
 0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  0  0  0  2  2  0  2  2  0  2  2
 0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  2  0  0  2  0  0  2  0  2  2  0  0  2  2  0  0  0  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  0  2  0  2  0  0  2  2  0  0  2  0  0  0  0  2  0  2  2  0  2  2  0  0  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+4x^34+92x^36+60x^38+137x^40+60x^42+70x^44+4x^46+30x^48+13x^52+1x^56+1x^68

The gray image is a code over GF(2) with n=80, k=9 and d=32.
This code was found by Heurico 1.16 in 0.0381 seconds.