The generator matrix

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

generates a code of length 12 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+117x^28+48x^30+399x^32+384x^33+288x^34+690x^36+1152x^37+432x^38+540x^40+33x^44+12x^48

The gray image is a linear code over GF(4) with n=48, k=6 and d=28.
This code was found by Heurico 1.16 in 0.0107 seconds.