The generator matrix

1 0 0 0 0 0 0 1 1 1 2 1 1 1 0 1 1 1 1 0 1 1 1 1 0 2 0 1 1 1 2 1 1 2 1 0 2 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 3 2 2 1 2 3 3 1 1 2 3 3 2 1 1 1 2 3 1 1 1
0 0 1 0 0 0 0 0 0 0 0 1 3 2 1 2 0 2 0 2 3 3 3 3 3 0 1 1 1 3 3 0 1 1 2 0 0 2
0 0 0 1 0 0 0 0 0 0 0 2 1 3 1 2 2 0 3 1 0 1 0 2 2 3 1 3 1 2 0 1 3 0 3 0 3 3
0 0 0 0 1 0 0 1 2 3 1 0 0 0 0 0 2 1 2 0 2 1 3 1 1 3 1 0 0 2 2 3 0 1 3 1 2 1
0 0 0 0 0 1 0 1 3 2 3 0 0 0 2 2 1 1 1 1 0 1 3 2 0 0 1 1 2 0 0 1 3 2 3 0 0 1
0 0 0 0 0 0 1 2 1 3 3 1 2 3 1 0 3 0 1 2 3 1 3 2 3 1 0 0 2 2 2 0 1 2 3 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+247x^28+664x^30+1307x^32+1886x^34+2541x^36+2936x^38+2717x^40+2044x^42+1187x^44+598x^46+180x^48+60x^50+9x^52+2x^54+3x^56+2x^58

The gray image is a code over GF(2) with n=76, k=14 and d=28.
This code was found by Heurico 1.10 in 6.66 seconds.