The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+231x^30+547x^32+839x^34+1120x^36+1346x^38+1346x^40+1192x^42+891x^44+429x^46+170x^48+57x^50+20x^52+2x^54+1x^60

The gray image is a code over GF(2) with n=78, k=13 and d=30.
This code was found by Heurico 1.16 in 5.12 seconds.