The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1
 0  1  0  1  a a+1 (a+1)X (a+1)X+1 (a+1)X+a+1 (a+1)X+a+1 (a+1)X  0
 0  0  1 a+1  a  1  1  0  a  0 a+1  X
 0  0  0  X  0  X  0 aX (a+1)X  X aX (a+1)X
 0  0  0  0  X (a+1)X (a+1)X  0 (a+1)X  X aX  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+87x^24+108x^25+336x^27+735x^28+528x^29+960x^30+3024x^31+2769x^32+3912x^33+5760x^34+9072x^35+5406x^36+9360x^37+8640x^38+9072x^39+4143x^40+1452x^41+147x^44+24x^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 1.57 seconds.