The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  0  1  1  1  X  1
 0  1  1  a a^2*X+a^2  0 a^2*X+1  a a^2*X+a^2  1  0  a a^2*X+1 a^2*X+a^2  X  X X+a  X  1  0 a*X+a^2 a*X  1 a^2*X+1
 0  0 a^2*X  0  X  0  X a*X a*X a*X a*X  X a^2*X a^2*X a^2*X  X a^2*X a*X a*X a*X a*X  X  0  X
 0  0  0  X a*X a*X  0 a*X  X  X  0  X a*X  X  0 a^2*X  X a^2*X a*X  X a*X a*X  X  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+321x^64+894x^68+1515x^72+1227x^76+111x^80+12x^84+9x^88+3x^92+3x^96

The gray image is a linear code over GF(4) with n=96, k=6 and d=64.
This code was found by Heurico 1.16 in 0.0293 seconds.