The generator matrix

 1  1
 0 a^2*X+1

generates a code of length 2 over F4[X]/(X^2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+24x^3+6x^4+144x^6+72x^7+9x^8

The gray image is a linear code over GF(4) with n=8, k=4 and d=3.
This code was found by Heurico 1.16 in 1.01e-007 seconds.