The generator matrix

 1  0  0  1  1  1 12  1  1  6  1  0  1 14
 0  1  0  4  1 11  1  2 15  1  6  1  3  1
 0  0  1  7  1  4  3  2  3  3  5  6  6  7
 0  0  0  8  8  8  8  8  0  0  0  8  0  8

generates a code of length 14 over Z16 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+222x^11+856x^12+1450x^13+3168x^14+1436x^15+819x^16+212x^17+16x^18+6x^19+4x^20+2x^21

The gray image is a code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.16 in 0.119 seconds.