The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+37x^14+50x^15+137x^16+160x^17+219x^18+312x^19+369x^20+496x^21+510x^22+508x^23+394x^24+320x^25+226x^26+152x^27+110x^28+48x^29+29x^30+2x^31+12x^32+3x^34+1x^36

The gray image is a code over GF(2) with n=44, k=12 and d=14.
This code was found by Heurico 1.16 in 0.351 seconds.