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.