The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+96x^32+86x^34+200x^36+124x^38+193x^40+136x^42+108x^44+36x^46+27x^48+2x^50+12x^52+3x^56

The gray image is a code over GF(2) with n=78, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0945 seconds.