The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+96x^31+158x^32+204x^33+323x^34+232x^35+331x^36+340x^37+221x^38+332x^39+229x^40+292x^41+326x^42+276x^43+286x^44+172x^45+146x^46+84x^47+10x^48+16x^49+7x^50+4x^51+7x^52+1x^54+1x^56+1x^64

The gray image is a code over GF(2) with n=78, k=12 and d=31.
This code was found by Heurico 1.16 in 49.2 seconds.