The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+160x^28+264x^30+724x^32+856x^34+1386x^36+1344x^38+1509x^40+864x^42+668x^44+248x^46+131x^48+8x^50+26x^52+3x^56

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 4.57 seconds.