The generator matrix

 1  0  0  0  1  1  1  1  1  1 a^2*X  1
 0  1  0  0  0  X  X a^2*X+1 a^2*X+1  a  1  1
 0  0  1  0  1 a^2*X+a a^2*X+a^2  a  0  1  a  a
 0  0  0  1 a^2  a  1  0  a  1 a^2 X+a^2
 0  0  0  0  X  0 a*X a^2*X  X a^2*X  X  0

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

Homogenous weight enumerator: w(x)=1x^0+333x^24+468x^25+144x^26+1056x^27+3612x^28+2448x^29+3264x^30+9504x^31+15690x^32+14040x^33+18144x^34+28512x^35+46752x^36+31824x^37+27072x^38+28512x^39+23559x^40+6516x^41+528x^42+132x^44+33x^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 19.5 seconds.