The generator matrix

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

generates a code of length 23 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+45x^14+295x^16+638x^18+192x^19+1836x^20+2048x^21+7403x^22+7808x^23+7411x^24+2048x^25+1928x^26+192x^27+628x^28+215x^30+68x^32+10x^34+1x^38+1x^40

The gray image is a code over GF(2) with n=184, k=15 and d=56.
This code was found by Heurico 1.16 in 3.92 seconds.