The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+195x^32+415x^34+553x^36+571x^38+656x^40+570x^42+572x^44+322x^46+188x^48+39x^50+10x^52+3x^54+1x^68

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 1.18 seconds.