The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+92x^7+267x^8+400x^9+716x^10+1320x^11+1844x^12+2288x^13+2556x^14+2272x^15+1779x^16+1328x^17+804x^18+408x^19+204x^20+80x^21+20x^22+4x^23+1x^24

The gray image is a code over GF(2) with n=28, k=14 and d=7.
This code was found by Heurico 1.16 in 3.43 seconds.