The generator matrix

 1  0  0  1  1  1  0  1  1  0  1  1  1  1
 0  1  0  1  0  1  1  0  2  0  0  0  2  0
 0  0  1  1  1  0  1  0  1  1  0  0  1  2
 0  0  0  2  0  0  0  0  2  2  0  2  0  2
 0  0  0  0  2  0  0  2  2  0  0  2  0  0
 0  0  0  0  0  2  0  2  2  2  0  0  0  0
 0  0  0  0  0  0  2  0  2  2  2  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+12x^8+28x^9+57x^10+80x^11+117x^12+140x^13+145x^14+160x^15+110x^16+84x^17+51x^18+16x^19+15x^20+4x^21+3x^22+1x^24

The gray image is a code over GF(2) with n=28, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00715 seconds.