The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  1  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  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  0

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

Homogenous weight enumerator: w(x)=1x^0+90x^4+192x^6+1179x^8+1368x^10+5064x^12+8160x^14+9447x^16+3920x^18+2226x^20+672x^22+413x^24+24x^26+12x^28

The gray image is a code over GF(2) with n=30, k=15 and d=4.
This code was found by Heurico 1.16 in 1.67 seconds.