The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+93x^14+100x^15+237x^16+328x^17+471x^18+616x^19+757x^20+968x^21+970x^22+1040x^23+790x^24+664x^25+438x^26+280x^27+250x^28+88x^29+73x^30+12x^31+12x^32+3x^34+1x^36

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 1.38 seconds.