The generator matrix

 1  0  1  1  1
 0  1  1  0  0
 0  0 2a+2  0  0
 0  0  0  2  0
 0  0  0  0  2

generates a code of length 5 over GR(16,4) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+15x^4+48x^6+90x^8+432x^10+1806x^12+1296x^14+6144x^15+5013x^16+1296x^18+243x^20

The gray image is a code over GF(4) with n=20, k=7 and d=4.
This code was found by Heurico 1.16 in 0.013 seconds.