The generator matrix

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

generates a code of length 12 over Z16 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+46x^6+128x^7+517x^8+1612x^9+5293x^10+12564x^11+25143x^12+12664x^13+5309x^14+1576x^15+510x^16+124x^17+39x^18+4x^19+5x^20+1x^22

The gray image is a code over GF(2) with n=96, k=16 and d=24.
This code was found by Heurico 1.16 in 1.97 seconds.