The generator matrix

 1  0  0  1  1  1 14  8  8  1  1
 0  1  0  1  2  3  2  1  1 12  8
 0  0  1  1  1  4  1  2  3 13  0
 0  0  0  2  8 10  6  6 12 14  4

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

Homogenous weight enumerator: w(x)=1x^0+64x^7+578x^8+2242x^9+7200x^10+12568x^11+7288x^12+2188x^13+544x^14+88x^15+5x^16+2x^17

The gray image is a code over GF(2) with n=88, k=15 and d=28.
This code was found by Heurico 1.16 in 0.969 seconds.