The generator matrix

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

generates a code of length 38 over Z4 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+36x^27+121x^28+242x^29+373x^30+460x^31+590x^32+760x^33+981x^34+1178x^35+1230x^36+1402x^37+1450x^38+1422x^39+1364x^40+1218x^41+1094x^42+798x^43+597x^44+408x^45+285x^46+190x^47+59x^48+62x^49+37x^50+12x^51+4x^52+4x^53+4x^54+2x^56

The gray image is a code over GF(2) with n=76, k=14 and d=27.
This code was found by Heurico 1.10 in 6.37 seconds.