The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+234x^30+526x^32+876x^34+1150x^36+1298x^38+1332x^40+1134x^42+897x^44+524x^46+189x^48+30x^50+1x^76

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 4.63 seconds.