The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  1
 0  X  0  0  0  0  0  X  X  X  X a*X a^2*X a*X  X  0 a*X a*X  X  0  0  X  0
 0  0  X  0  0  0  X a^2*X a^2*X  X a*X a*X  X  X a*X  X  X a^2*X  0 a^2*X  X a*X  0
 0  0  0  X  0  0 a^2*X  X  0 a*X a*X a*X  0 a^2*X  X a*X  X a*X a^2*X a^2*X a*X  0 a^2*X
 0  0  0  0  X  0  X a^2*X a*X  0  X a^2*X a*X a*X a^2*X  0  0 a*X a*X  0 a^2*X a*X a*X
 0  0  0  0  0  X a^2*X  X a^2*X  X a^2*X  X  X a*X  0 a^2*X  0  0 a*X  0  X  X 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+144x^52+324x^56+438x^60+768x^63+543x^64+4608x^67+657x^68+6912x^71+762x^72+639x^76+420x^80+135x^84+30x^88+3x^92

The gray image is a linear code over GF(4) with n=92, k=7 and d=52.
This code was found by Heurico 1.16 in 0.716 seconds.