The generator matrix

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

generates a code of length 38 over Z4 who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+34x^25+186x^26+360x^27+562x^28+852x^29+1271x^30+1786x^31+2282x^32+2942x^33+3787x^34+4682x^35+5254x^36+5684x^37+5932x^38+5800x^39+5331x^40+4582x^41+3892x^42+3132x^43+2450x^44+1732x^45+1155x^46+794x^47+449x^48+282x^49+151x^50+82x^51+54x^52+20x^53+10x^54+4x^55+1x^56

The gray image is a code over GF(2) with n=76, k=16 and d=25.
This code was found by Heurico 1.10 in 88.9 seconds.