The generator matrix

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

generates a code of length 12 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+39x^24+177x^28+147x^32+3282x^36+291x^40+141x^44+18x^48

The gray image is a linear code over GF(4) with n=48, k=6 and d=24.
This code was found by Heurico 1.16 in 0.0152 seconds.