The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+21x^14+68x^15+162x^16+208x^17+339x^18+836x^19+1503x^20+2968x^21+4120x^22+2996x^23+1530x^24+864x^25+356x^26+188x^27+128x^28+56x^29+27x^30+8x^31+3x^32+1x^34+1x^36

The gray image is a code over GF(2) with n=176, k=14 and d=56.
This code was found by Heurico 1.16 in 1.1 seconds.