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

generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+108x^60+189x^64+162x^68+3222x^72+147x^76+129x^80+96x^84+24x^88+15x^92+3x^96

The gray image is a linear code over GF(4) with n=96, k=6 and d=60.
This code was found by Heurico 1.16 in 0.0562 seconds.