The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1
 0  1  1  a a^2  0 a^2*X+1  a a^2*X+a^2  1  a  a
 0  0 a^2*X  0  0  0  X  0  X  X a*X a*X
 0  0  0  X  0  0 a^2*X  X  X a^2*X  0 a*X
 0  0  0  0 a^2*X  0  X a^2*X  0 a^2*X a*X  X
 0  0  0  0  0  X a^2*X a^2*X  X a*X a*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+378x^24+972x^28+3072x^30+3087x^32+18432x^34+6504x^36+27648x^38+4878x^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 1.82 seconds.