The generator matrix

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

generates a code of length 11 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+44x^4+49x^6+214x^8+512x^9+204x^10+6144x^11+204x^12+512x^13+214x^14+49x^16+44x^18+1x^22

The gray image is a code over GF(2) with n=88, k=13 and d=16.
This code was found by Heurico 1.16 in 0.0211 seconds.