The generator matrix

 1  0  1  1  1  4  2  8  1  1  1
 0  1  1  0  3  1 14  0 10  2  0
 0  0  2  0  2  4  2  2  4 12  4
 0  0  0  2  2  6  6  4  2  0 12

generates a code of length 11 over Z16 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+52x^7+409x^8+1184x^9+3942x^10+5208x^11+3942x^12+1184x^13+409x^14+52x^15+1x^22

The gray image is a code over GF(2) with n=88, k=14 and d=28.
This code was found by Heurico 1.16 in 0.248 seconds.