The generator matrix

 1  1  1  1  1  1  1  1  1  1  1
 0 12  0  0  0  0  0  8  8 12 12
 0  0 12  0  0  0  4  4 12  0  8
 0  0  0 12  0  4  4  4  0  8  8
 0  0  0  0 12  4  0  4 12  8  0
 0  0  0  0  0  8  0  0  8  0  8
 0  0  0  0  0  0  8  0  8  8  8

generates a code of length 11 over Z16 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+173x^6+160x^7+234x^8+384x^9+616x^10+13248x^11+616x^12+384x^13+234x^14+160x^15+173x^16+1x^22

The gray image is a code over GF(2) with n=88, k=14 and d=24.
This code was found by Heurico 1.16 in 2.26 seconds.