The generator matrix

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

generates a code of length 4 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+48x^9+60x^12+144x^13+3x^16

The gray image is a linear code over GF(4) with n=16, k=4 and d=9.
This code was found by Heurico 1.16 in 6.87e-008 seconds.