The generator matrix

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

generates a code of length 21 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+81x^14+108x^15+202x^16+286x^17+709x^18+1622x^19+3100x^20+4130x^21+3092x^22+1666x^23+744x^24+306x^25+200x^26+58x^27+44x^28+14x^29+11x^30+2x^31+5x^32+3x^34

The gray image is a code over GF(2) with n=168, k=14 and d=56.
This code was found by Heurico 1.16 in 1.24 seconds.