The generator matrix

 1  0  0  0  0  1  1  1  2  0  1  1  1  1  1  0  2  1  1  1  1  2  0  1  2  1  1  1  1  1  1  1  1  1  1  1  0  2  1
 0  1  0  0  0  0  0  0  0  0  0  2  2  3  1  1  1  2  3  1  3  2  1  2  1  0  1  3  1  1  0  2  2  1  3  1  1  1  1
 0  0  1  0  0  0  1  1  1  2  2  1  2  0  3  3  3  1  1  3  0  1  1  3  2  3  3  1  1  1  0  0  3  1  3  2  3  1  0
 0  0  0  1  0  1  1  0  3  2  0  0  3  3  0  1  2  1  3  1  2  3  0  1  0  3  2  2  0  2  1  3  0  1  1  0  3  2  0
 0  0  0  0  1  1  2  3  1  1  1  0  0  3  3  2  3  2  1  0  3  3  0  1  2  3  2  0  1  1  3  3  2  0  2  0  2  1  1
 0  0  0  0  0  2  0  2  2  2  0  2  0  0  2  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  0  2  2  2  0  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+147x^32+272x^34+354x^36+290x^38+292x^40+266x^42+236x^44+118x^46+56x^48+14x^50+2x^52

The gray image is a code over GF(2) with n=78, k=11 and d=32.
This code was found by Heurico 1.16 in 0.306 seconds.