The generator matrix

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

generates a code of length 13 over Z16 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+138x^11+204x^12+376x^13+160x^14+116x^15+19x^16+8x^17+2x^19

The gray image is a code over GF(2) with n=104, k=10 and d=44.
This code was found by Heurico 1.16 in 0.00739 seconds.