The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^8+160x^9+108x^10+134x^12+320x^13+136x^14+43x^16+32x^17+12x^18+2x^20

The gray image is a code over GF(2) with n=24, k=10 and d=8.
This code was found by Heurico 1.16 in 0.0209 seconds.