The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+225x^28+320x^30+998x^32+1248x^34+2520x^36+2704x^38+3217x^40+2192x^42+1718x^44+624x^46+445x^48+80x^50+80x^52+11x^56+1x^60

The gray image is a code over GF(2) with n=78, k=14 and d=28.
This code was found by Heurico 1.16 in 16.7 seconds.