The generator matrix

 1  0  1  1  1 12  1  6  6  1  1  2  2  1  8 12
 0  1  1  0  3  1  6  1  1  3 13  1 12 15 12  2
 0  0  2  6  0  2  4  4  6  2  0  2  2 14  2  2
 0  0  0 12  0 12  4 12  8 12  4  8  4  0  8  4
 0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8

generates a code of length 16 over Z16 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+223x^12+520x^13+1864x^14+3424x^15+4294x^16+3504x^17+1840x^18+480x^19+201x^20+8x^21+24x^22+1x^24

The gray image is a code over GF(2) with n=128, k=14 and d=48.
This code was found by Heurico 1.16 in 0.466 seconds.