The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^8+100x^9+250x^10+288x^11+370x^12+612x^13+634x^14+672x^15+379x^16+300x^17+254x^18+64x^19+62x^20+12x^21+14x^22

The gray image is a code over GF(2) with n=28, k=12 and d=8.
This code was found by Heurico 1.16 in 0.138 seconds.