The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^28+106x^29+325x^30+330x^31+521x^32+694x^33+769x^34+894x^35+1031x^36+1214x^37+1308x^38+1592x^39+1358x^40+1362x^41+1144x^42+1014x^43+848x^44+604x^45+459x^46+228x^47+228x^48+112x^49+79x^50+36x^51+25x^52+4x^53+12x^54+2x^55+4x^56

The gray image is a code over GF(2) with n=78, k=14 and d=28.
This code was found by Heurico 1.10 in 6.67 seconds.