The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+9x^8+44x^9+53x^10+20x^11+6x^12+20x^13+42x^14+44x^15+16x^16+1x^18

The gray image is a code over GF(2) with n=24, k=8 and d=8.
This code was found by Heurico 1.16 in 0.00097 seconds.