The generator matrix

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

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+324x^24+480x^25+144x^26+1056x^27+3648x^28+2400x^29+3264x^30+9504x^31+15633x^32+14112x^33+18144x^34+28512x^35+46800x^36+31776x^37+27072x^38+28512x^39+23532x^40+6528x^41+528x^42+144x^44+30x^48

The gray image is a linear code over GF(4) with n=48, k=9 and d=24.
This code was found by Heurico 1.16 in 15.4 seconds.