The generator matrix

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

generates a code of length 38 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+61x^28+86x^29+180x^30+246x^31+367x^32+414x^33+507x^34+578x^35+599x^36+692x^37+637x^38+724x^39+648x^40+628x^41+548x^42+444x^43+311x^44+214x^45+154x^46+54x^47+56x^48+14x^49+15x^50+2x^51+5x^52+5x^54+2x^58

The gray image is a code over GF(2) with n=76, k=13 and d=28.
This code was found by Heurico 1.16 in 4.25 seconds.