The generator matrix
1 0 1
0 1 (a+1)X+1
generates a code of length 3 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+36x^6+9x^8+96x^9+108x^10+6x^12
The gray image is a linear code over GF(4) with n=12, k=4 and d=6.
This code was found by Heurico 1.16 in 1.01e-007 seconds.