The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  1  1  1
 0  1  0  1  0  1  1  0  0  0  0  0  0  0
 0  0  1  1  1  0  1  0  0  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  0
 0  0  0  0  0  0  0  0  0  2  0  0  2  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  0  0  0  2  2  0

generates a code of length 14 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+90x^4+204x^6+1191x^8+1756x^10+2048x^11+3276x^12+6144x^13+3480x^14+6144x^15+2847x^16+2048x^17+2328x^18+762x^20+412x^22+25x^24+12x^26

The gray image is a code over GF(2) with n=28, k=15 and d=4.
This code was found by Heurico 1.16 in 1.73 seconds.