The generator matrix

 1  0  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  X  X  1  1  1
 0  1  1  a a^2*X+a^2  0 a^2*X+1 a^2*X+a^2  X  a  1 a^2*X+1  1  X X+a X+a a*X+a^2 a*X+a^2  1  1  0  X a*X
 0  0 a^2*X a*X  X  X  0 a^2*X a*X a^2*X a^2*X  X a*X a^2*X  X  0 a*X  0 a*X  X a*X  X  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+51x^64+288x^65+108x^68+192x^69+60x^72+288x^73+36x^76

The gray image is a linear code over GF(4) with n=92, k=5 and d=64.
This code was found by Heurico 1.16 in 0.016 seconds.