The generator matrix

 1  1  1
 0  X  0
 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+27x^8+192x^9+27x^12

The gray image is a linear code over GF(4) with n=12, k=4 and d=4.
This code was found by Heurico 1.16 in -6.87e-008 seconds.