The generator matrix

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

generates a code of length 15 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+78x^4+13x^6+715x^8+286x^10+1716x^12+1287x^14+8192x^15+1287x^16+1716x^18+286x^20+715x^22+13x^24+78x^26+1x^30

The gray image is a code over GF(2) with n=30, k=14 and d=4.
This code was found by Heurico 1.16 in 0.732 seconds.