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.