The generator matrix

 1  0  1  1  1 14  1  1  8  1  1
 0  1 11  6  5  1  5  0  1 13  3
 0  0 12  0  0  8  4 12  4  0  4
 0  0  0 12  0 12  4  4  8  4 12
 0  0  0  0  8  0  0  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+32x^7+111x^8+512x^9+1936x^10+3008x^11+1943x^12+512x^13+96x^14+32x^15+8x^16+1x^20

The gray image is a code over GF(2) with n=88, k=13 and d=28.
This code was found by Heurico 1.16 in 0.0477 seconds.