The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+79x^4+168x^6+834x^8+851x^10+512x^11+1326x^12+2048x^13+837x^14+3072x^15+837x^16+2048x^17+1326x^18+512x^19+851x^20+834x^22+168x^24+79x^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 0.506 seconds.