The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1
0 X 0 0 0 0 0 X X X X a*X a^2*X a*X X a^2*X a^2*X X a*X X X X 0 0
0 0 X 0 0 0 X a^2*X a^2*X X a*X a*X X X 0 0 a*X a*X a^2*X X a^2*X a*X a^2*X X
0 0 0 X 0 0 a^2*X X 0 a*X a*X a*X 0 a^2*X a^2*X X a^2*X 0 X a*X X X 0 X
0 0 0 0 X 0 X a^2*X a*X 0 X a^2*X a*X a*X a*X X a^2*X X X a^2*X a*X a*X X X
0 0 0 0 0 X a^2*X X a^2*X X a^2*X X X a*X X 0 0 0 X X a*X a*X a*X a*X
generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+219x^56+387x^60+474x^64+768x^66+549x^68+4608x^70+636x^72+6912x^74+741x^76+630x^80+315x^84+117x^88+24x^92+3x^96
The gray image is a linear code over GF(4) with n=96, k=7 and d=56.
This code was found by Heurico 1.16 in 3.16 seconds.