The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  2  0  1  0  1  0  1  1  0  1  1  1  0  2  0  1  2  2  0  0  1  2  0  1  1  1
 0  1  0  0  0  1  1  1  0  0  3  3  1  1  1  2  0  1  2  1  2  1  2  2  1  1  0  1  1  1  1  1  3  0  0  0  1  1
 0  0  1  0  1  1  0  1  0  1  1  2  0  3  1  1  2  1  2  0  2  2  1  1  2  1  1  3  0  1  3  0  2  0  1  1  0  3
 0  0  0  1  1  0  1  1  1  0  1  0  1  2  0  1  0  3  3  3  1  2  1  0  2  2  0  3  1  1  2  0  3  1  3  2  0  1
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  0  2  2  2  0  2  0  0  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  2  0  2  0  2  2  2  0  0  0  2  0  2  0  0
 0  0  0  0  0  0  0  2  0  0  2  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  2  2  0  0  0  2  2  2  2  0  0  2
 0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  2  2  2  0  2  2  0  2  2  2  2  0  0  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  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+327x^28+538x^30+1336x^32+1750x^34+2801x^36+2796x^38+2797x^40+2036x^42+1193x^44+506x^46+215x^48+54x^50+31x^52+3x^56

The gray image is a code over GF(2) with n=76, k=14 and d=28.
This code was found by Heurico 1.16 in 48.3 seconds.