The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+91x^4+1001x^8+3003x^12+8192x^14+3003x^16+1001x^20+91x^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 0.729 seconds.