The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+43x^30+88x^31+141x^32+198x^33+209x^34+306x^35+330x^36+276x^37+298x^38+316x^39+327x^40+330x^41+328x^42+244x^43+170x^44+186x^45+137x^46+68x^47+50x^48+32x^49+7x^50+2x^51+4x^52+2x^53+2x^54+1x^56

The gray image is a code over GF(2) with n=78, k=12 and d=30.
This code was found by Heurico 1.10 in 0.406 seconds.