The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^30+78x^31+183x^32+226x^33+212x^34+224x^35+301x^36+334x^37+277x^38+352x^39+305x^40+278x^41+278x^42+296x^43+215x^44+162x^45+121x^46+74x^47+75x^48+24x^49+17x^50+8x^52+1x^58

The gray image is a code over GF(2) with n=78, k=12 and d=30.
This code was found by Heurico 1.16 in 1.07 seconds.