The generator matrix
1 0 1 1 1 1 1
0 1 1 a (a+1)X+a+1 X 0
0 0 (a+1)X X aX 0 X
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+45x^16+192x^18+108x^20+576x^22+90x^24+12x^28
The gray image is a linear code over GF(4) with n=28, k=5 and d=16.
This code was found by Heurico 1.16 in -1.01e-007 seconds.