The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  1  1  2  2  1  2  4  4  2  1  1
 0 12  0  0  0  0  0  0  8  4 12 12  4  0  4  8  8  4 12 12 12  8
 0  0 12  0  0  0  0  8 12  0  4  4  4 12  8  4  8  0  0  8  4  0
 0  0  0 12  0  0  0 12  8  8 12  4  4  8  4 12  8 12  0  0  0  0
 0  0  0  0 12  0  4  4 12 12 12  4  8 12  0  0  4 12  0 12 12  0
 0  0  0  0  0 12  4  8  8  0 12  4 12  4  0  8  0  4  8 12  0  4
 0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  0  8  8  0  0  0

generates a code of length 22 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+67x^14+132x^15+254x^16+350x^17+693x^18+1144x^19+2720x^20+6512x^21+8867x^22+6608x^23+2819x^24+1228x^25+671x^26+296x^27+203x^28+96x^29+70x^30+12x^31+18x^32+6x^33+1x^36

The gray image is a code over GF(2) with n=176, k=15 and d=56.
This code was found by Heurico 1.16 in 4.7 seconds.