The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+134x^27+227x^28+314x^29+497x^30+596x^31+836x^32+976x^33+1073x^34+1308x^35+1385x^36+1490x^37+1530x^38+1364x^39+1158x^40+996x^41+834x^42+602x^43+434x^44+290x^45+149x^46+88x^47+53x^48+28x^49+13x^50+4x^51+1x^52+2x^53+1x^60

The gray image is a code over GF(2) with n=74, k=14 and d=27.
This code was found by Heurico 1.10 in 241 seconds.