The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+74x^14+116x^15+254x^16+344x^17+465x^18+614x^19+731x^20+926x^21+978x^22+1006x^23+854x^24+702x^25+456x^26+290x^27+196x^28+74x^29+68x^30+22x^31+11x^32+2x^33+7x^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 1.47 seconds.