The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  2  1  1
 0  1  0  0  1  0  0  1  1  0  0  0  0  0
 0  0  1  0  1  0  1  0  1  0  0  0  0  0
 0  0  0  1  1  1  0  0  1  0  0  0  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+103x^4+336x^6+1605x^8+3392x^10+6995x^12+7904x^14+6995x^16+3392x^18+1605x^20+336x^22+103x^24+1x^28

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 1.62 seconds.