The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^30+102x^31+147x^32+140x^33+223x^34+286x^35+250x^36+316x^37+338x^38+336x^39+340x^40+372x^41+275x^42+240x^43+220x^44+180x^45+102x^46+58x^47+56x^48+16x^49+13x^50+2x^51+10x^52+6x^54+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 1.25 seconds.