The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+61x^14+110x^15+260x^16+364x^17+482x^18+600x^19+774x^20+900x^21+921x^22+1052x^23+810x^24+692x^25+502x^26+264x^27+194x^28+92x^29+81x^30+22x^31+9x^32+1x^38

The gray image is a code over GF(2) with n=44, k=13 and d=14.
This code was found by Heurico 1.16 in 1.59 seconds.