The generator matrix
1 0 0 1 1 1 1 (a+1)X 1 1 1 1
0 1 0 (a+1)X 1 X (a+1)X+1 1 (a+1)X+a aX+a a+1 aX+a+1
0 0 1 1 a+1 (a+1)X+a a 1 X+1 aX+a+1 X+a+1 X
generates a code of length 12 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 31.
Homogenous weight enumerator: w(x)=1x^0+576x^31+225x^32+1152x^35+576x^36+1344x^39+216x^40+6x^48
The gray image is a linear code over GF(4) with n=48, k=6 and d=31.
This code was found by Heurico 1.16 in 5.28 seconds.