The generator matrix

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

generates a code of length 8 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+96x^22+60x^24+96x^26+3x^32

The gray image is a linear code over GF(4) with n=32, k=4 and d=22.
As d=22 is an upper bound for linear (32,4,4)-codes, this code is optimal over F4[X,sigma]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in -3.24e-008 seconds.