The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+79x^4+168x^6+845x^8+1376x^10+3683x^12+4080x^14+3683x^16+1376x^18+845x^20+168x^22+79x^24+1x^28

The gray image is a code over GF(2) with n=28, k=14 and d=4.
This code was found by Heurico 1.16 in 0.479 seconds.