The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  2  1  0  0  1  1  0  2  2  0  1  1  1  2  0  2  1  1  0  1  2  0  0  2  0  1  1
 0  1  0  0  0  0  0  0  0  3  1  1  2  1  1  1  1  3  1  1  1  2  1  2  3  1  2  2  1  2  0  0  1  1  1  2  0  3  0
 0  0  1  0  0  0  1  1  1  1  1  2  1  3  1  1  0  0  3  0  3  1  0  1  2  0  1  2  3  2  1  3  0  2  1  1  1  3  0
 0  0  0  1  0  1  1  0  1  0  0  2  3  1  3  2  2  0  3  1  0  2  1  3  3  2  1  1  3  1  0  2  1  1  2  3  2  1  0
 0  0  0  0  1  1  0  1  1  1  0  1  2  3  3  0  2  3  2  3  1  1  0  1  3  2  0  2  1  0  1  0  0  0  1  2  1  2  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  2  0  2  0  2  0  0  0  2  0  0  0  0  0  2  2  0  2  2  0  0  2  2  2  2  0
 0  0  0  0  0  0  2  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  2  0  0  0  2  0  0  0  2  0  2  0  2  2  0  0  2
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  0  2  2  2  0  0  0  2  2  2  0  0  0  0  2  2  2  0  2  2
 0  0  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  2  2  2  0  2  0  2  2  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+61x^28+114x^29+236x^30+362x^31+505x^32+606x^33+817x^34+914x^35+1062x^36+1292x^37+1354x^38+1508x^39+1432x^40+1398x^41+1194x^42+1012x^43+841x^44+586x^45+376x^46+274x^47+182x^48+90x^49+109x^50+26x^51+12x^52+8x^53+10x^54+2x^57

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 31.2 seconds.