The generator matrix

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

generates a code of length 23 over F4[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+135x^52+72x^54+333x^56+696x^58+615x^60+4176x^62+2295x^64+13296x^66+5847x^68+19176x^70+5964x^72+11736x^74+609x^76+372x^80+186x^84+27x^88

The gray image is a linear code over GF(4) with n=92, k=8 and d=52.
This code was found by Heurico 1.16 in 5.64 seconds.