The generator matrix

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

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+330x^24+396x^28+495x^32+13608x^36+990x^40+396x^44+168x^48

The gray image is a linear code over GF(4) with n=48, k=7 and d=24.
This code was found by Heurico 1.16 in 0.227 seconds.