The generator matrix

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

generates a code of length 18 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+21x^14+42x^15+28x^16+24x^17+28x^18+28x^19+30x^20+24x^21+13x^22+10x^23+5x^24+2x^26

The gray image is a code over GF(2) with n=36, k=8 and d=14.
This code was found by Heurico 1.16 in 0.00227 seconds.