The generator matrix

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

generates a code of length 37 over Z4 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+20x^27+100x^28+174x^29+287x^30+346x^31+425x^32+516x^33+501x^34+632x^35+674x^36+692x^37+763x^38+704x^39+611x^40+512x^41+423x^42+304x^43+195x^44+142x^45+66x^46+38x^47+39x^48+12x^49+8x^50+4x^51+3x^52

The gray image is a code over GF(2) with n=74, k=13 and d=27.
This code was found by Heurico 1.10 in 1.66 seconds.