The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+227x^28+724x^30+1269x^32+1874x^34+2558x^36+2852x^38+2814x^40+2058x^42+1202x^44+506x^46+228x^48+44x^50+20x^52+6x^54+1x^60

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 33.8 seconds.