The generator matrix

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

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+33x^28+75x^32+822x^36+48x^40+33x^44+12x^48

The gray image is a linear code over GF(4) with n=48, k=5 and d=28.
This code was found by Heurico 1.16 in 6.87e-008 seconds.