The generator matrix

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

generates a code of length 36 over Z4 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+102x^27+186x^28+252x^29+375x^30+404x^31+533x^32+550x^33+560x^34+680x^35+740x^36+768x^37+678x^38+626x^39+541x^40+418x^41+264x^42+216x^43+154x^44+58x^45+43x^46+18x^47+20x^48+2x^51+2x^53+1x^56

The gray image is a code over GF(2) with n=72, k=13 and d=27.
This code was found by Heurico 1.10 in 174 seconds.