The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  0
 0  1  1  a a+1  0 (a+1)X+1  a (a+1)X+a+1  1  0  1
 0  0 (a+1)X  0  0  0  X  0  X (a+1)X (a+1)X (a+1)X
 0  0  0  X  0  0 (a+1)X  X  X  X  X  0
 0  0  0  0 (a+1)X  0  X (a+1)X aX  0 (a+1)X  X
 0  0  0  0  0  X (a+1)X (a+1)X aX (a+1)X  X 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+330x^24+384x^27+396x^28+2304x^30+3456x^31+495x^32+13824x^34+10368x^35+1320x^36+20736x^38+10368x^39+990x^40+396x^44+168x^48

The gray image is a linear code over GF(4) with n=48, k=8 and d=24.
This code was found by Heurico 1.16 in 1.88 seconds.