The generator matrix
1 0 1
0 1 (a+1)X+1
0 0 X
generates a code of length 3 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+9x^4+144x^6+27x^8+384x^9+432x^10+27x^12
The gray image is a linear code over GF(4) with n=12, k=5 and d=4.
This code was found by Heurico 1.16 in 1.01e-007 seconds.