The generator matrix

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

generates a code of length 23 over F4[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+54x^64+72x^68+126x^72+3x^80

The gray image is a linear code over GF(4) with n=92, k=4 and d=64.
This code was found by Heurico 1.16 in -1.01e-007 seconds.