The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+56x^32+50x^33+60x^34+96x^35+73x^36+88x^37+74x^38+86x^39+74x^40+68x^41+66x^42+54x^43+38x^44+40x^45+46x^46+18x^47+13x^48+10x^49+10x^50+2x^51+1x^52

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 0.0814 seconds.