The generator matrix

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

generates a code of length 39 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+62x^28+286x^30+581x^32+812x^34+1058x^36+1291x^38+1269x^40+1126x^42+869x^44+485x^46+231x^48+89x^50+23x^52+6x^54+2x^56+1x^58

The gray image is a code over GF(2) with n=78, k=13 and d=28.
This code was found by Heurico 1.10 in 1.72 seconds.