The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+65x^28+98x^29+231x^30+260x^31+379x^32+444x^33+410x^34+510x^35+582x^36+702x^37+699x^38+728x^39+636x^40+600x^41+521x^42+460x^43+317x^44+190x^45+149x^46+84x^47+64x^48+12x^49+36x^50+6x^51+4x^52+2x^53+1x^54+1x^58

The gray image is a code over GF(2) with n=76, k=13 and d=28.
This code was found by Heurico 1.10 in 1.72 seconds.