The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+31x^28+118x^29+199x^30+264x^31+339x^32+398x^33+477x^34+530x^35+664x^36+736x^37+678x^38+672x^39+652x^40+664x^41+535x^42+364x^43+303x^44+234x^45+139x^46+88x^47+56x^48+26x^49+19x^50+2x^51+2x^52+1x^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 4.31 seconds.