The generator matrix

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

generates a code of length 18 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+57x^16+32x^18+24x^20+14x^24

The gray image is a code over GF(2) with n=36, k=7 and d=16.
This code was found by Heurico 1.16 in 0.00175 seconds.