The generator matrix

1 0 0 0 0 1 1 1 1 1 1 1 0 1
0 1 0 0 0 1 0 1 2 3 1 0 1 0
0 0 1 0 0 1 0 2 1 1 3 1 2 0
0 0 0 1 0 1 0 3 3 2 1 1 0 0
0 0 0 0 1 1 3 1 0 2 0 1 1 0
0 0 0 0 0 2 2 0 2 2 0 0 0 0

generates a code of length 14 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+57x^8+58x^9+130x^10+154x^11+197x^12+284x^13+248x^14+324x^15+214x^16+162x^17+122x^18+34x^19+43x^20+8x^21+12x^22

The gray image is a code over GF(2) with n=28, k=11 and d=8.
This code was found by Heurico 1.10 in 0.015 seconds.