The generator matrix
1 0 1 1 1 1 1 X 1 1 1 aX
0 1 (a+1)X+1 a X aX+1 X+a 1 aX X+1 aX+a 1
generates a code of length 12 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 35.
Homogenous weight enumerator: w(x)=1x^0+144x^35+60x^36+48x^39+3x^48
The gray image is a linear code over GF(4) with n=48, k=4 and d=35.
As d=35 is an upper bound for linear (48,4,4)-codes, this code is optimal over F4[X,sigma]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in -1.01e-007 seconds.