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.