The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+106x^28+110x^29+283x^30+362x^31+560x^32+568x^33+766x^34+930x^35+1045x^36+1286x^37+1310x^38+1518x^39+1312x^40+1464x^41+1108x^42+1012x^43+836x^44+578x^45+519x^46+246x^47+205x^48+80x^49+102x^50+26x^51+29x^52+10x^53+8x^54+2x^55+2x^56

The gray image is a code over GF(2) with n=78, k=14 and d=28.
This code was found by Heurico 1.16 in 32.2 seconds.