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.