The generator matrix

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

generates a code of length 15 over Z16 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+38x^11+94x^12+122x^13+428x^14+700x^15+423x^16+132x^17+48x^18+30x^19+26x^20+2x^21+4x^22

The gray image is a code over GF(2) with n=120, k=11 and d=44.
This code was found by Heurico 1.16 in 11.9 seconds.