The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+140x^7+663x^8+2420x^9+6608x^10+13048x^11+6695x^12+2440x^13+608x^14+124x^15+16x^16+4x^17+1x^20

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 8.48 seconds.