The generator matrix

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

generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+42x^64+96x^68+192x^69+36x^72+576x^73+27x^76+27x^80+6x^84+6x^88+15x^92

The gray image is a linear code over GF(4) with n=96, k=5 and d=64.
This code was found by Heurico 1.16 in 0 seconds.