The generator matrix

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

generates a code of length 23 over F4[X]/(X^2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+444x^63+162x^64+288x^65+240x^66+828x^67+204x^68+192x^69+468x^71+210x^72+288x^73+144x^74+564x^75+60x^76+3x^80

The gray image is a linear code over GF(4) with n=92, k=6 and d=63.
This code was found by Heurico 1.16 in 0.015 seconds.