The generator matrix

 1  0  1  1  1  1  1  1  1  0  0  1  1  1  1  1  1  1  1  0  1  0  1  1
 0  1  1  a a^2  0 a^2*X+1  a a^2*X+a^2  1  1  0 a^2*X+1  a a^2*X+a^2 a^2*X+1  0  a a^2*X+a^2  1 a^2*X+a^2  1  0 a^2*X+1
 0  0 a^2*X  0  0  0  0  X a*X  X a*X a*X a^2*X  X a^2*X  0 a*X a^2*X  X  0  X  X  0 a^2*X
 0  0  0  X  0  0  X a^2*X a^2*X a*X  X  0 a^2*X a^2*X a*X a*X a*X a^2*X  0  0 a*X  0  0 a^2*X
 0  0  0  0 a^2*X  0 a*X  0  X  X  X a*X a^2*X  X  0  X a^2*X  0 a^2*X  0 a^2*X  X  X a*X
 0  0  0  0  0  X a*X  X a*X a*X a^2*X  X  X  0  0  0 a*X a^2*X  0  X a^2*X a^2*X a^2*X a^2*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+48x^57+453x^60+720x^61+999x^64+4320x^65+3156x^68+12960x^69+5889x^72+19440x^73+4584x^76+11664x^77+597x^80+336x^84+132x^88+15x^92+3x^96

The gray image is a linear code over GF(4) with n=96, k=8 and d=56.
This code was found by Heurico 1.16 in 36.9 seconds.