The generator matrix

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

generates a code of length 21 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+32x^14+48x^15+94x^16+128x^17+164x^18+208x^19+220x^20+256x^21+228x^22+208x^23+172x^24+128x^25+76x^26+48x^27+20x^28+12x^30+5x^32

The gray image is a code over GF(2) with n=42, k=11 and d=14.
This code was found by Heurico 1.16 in 0.0866 seconds.