The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^28+134x^30+423x^32+446x^34+636x^36+632x^38+646x^40+456x^42+396x^44+114x^46+92x^48+10x^50+8x^52+6x^56

The gray image is a code over GF(2) with n=76, k=12 and d=28.
This code was found by Heurico 1.16 in 1.13 seconds.