The generator matrix

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

generates a code of length 6 over GR(16,4) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+18x^4+48x^6+135x^8+576x^10+540x^12+2592x^14+6144x^15+1215x^16+29760x^18+18432x^19+1458x^20+3888x^22+729x^24

The gray image is a code over GF(4) with n=24, k=8 and d=4.
This code was found by Heurico 1.16 in 0.21 seconds.