The generator matrix

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

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+51x^24+48x^27+303x^28+384x^30+432x^31+825x^32+768x^33+2304x^34+1296x^35+1518x^36+2304x^37+3456x^38+1296x^39+1227x^40+147x^44+24x^48

The gray image is a linear code over GF(4) with n=48, k=7 and d=24.
This code was found by Heurico 1.16 in 0.125 seconds.