The generator matrix

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

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+414x^28+576x^30+1539x^32+3456x^34+2892x^36+5184x^38+2268x^40+54x^44

The gray image is a linear code over GF(4) with n=48, k=7 and d=28.
This code was found by Heurico 1.16 in 0.0846 seconds.