The generator matrix

 1  0  0  1  1  1 (a+1)X
 0  1  0 (a+1)X  1 (a+1)X+1  1
 0  0  1  1 X+1  X  1

generates a code of length 7 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+273x^16+672x^18+504x^20+2016x^22+630x^24

The gray image is a linear code over GF(4) with n=28, k=6 and d=16.
This code was found by Heurico 1.16 in -1.01e-007 seconds.