The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+31x^14+44x^15+118x^16+192x^17+255x^18+292x^19+399x^20+528x^21+421x^22+412x^23+418x^24+384x^25+288x^26+140x^27+80x^28+48x^29+27x^30+8x^31+7x^32+1x^34+1x^36+1x^38

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 0.353 seconds.