The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+41x^16+52x^17+76x^18+108x^19+97x^20+110x^21+89x^22+84x^23+90x^24+104x^25+80x^26+44x^27+25x^28+6x^29+9x^30+4x^31+2x^32+2x^34

The gray image is a code over GF(2) with n=44, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0291 seconds.