The generator matrix

 1  0  1  1  1 14  1  1  8  1  1  6  1  1  1  1  1  0  1  2  1  1
 0  1 11  6  5  1  0  3  1 14 13  1  8  6 12  8  5  1 14  8  6  0
 0  0 12  0  4  0  4  0  4  4  0  4  8 12  0  4 12  4  0  8  0  0
 0  0  0 12  4  4  4  0  0  0  4  4  4 12  8  8 12 12  4 12  0  0
 0  0  0  0  8  0  0  0  0  8  0  8  0  0  8  0  8  8  0  8  0  0
 0  0  0  0  0  8  0  0  8  8  8  8  0  8  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  0  0  0  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+51x^14+32x^15+334x^16+208x^17+1253x^18+2512x^19+6220x^20+12608x^21+18970x^22+12608x^23+6476x^24+2512x^25+1174x^26+208x^27+260x^28+32x^29+51x^30+21x^32+5x^34

The gray image is a code over GF(2) with n=176, k=16 and d=56.
This code was found by Heurico 1.16 in 7.68 seconds.