The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  2  1  1  1  1
 0  2  0  0  0  0  0  2  2  2  2 2a 2a+2 2a  2  0 2a 2a  2  0  0  2  0
 0  0  2  0  0  0  2 2a+2 2a+2  2 2a 2a  2  2 2a  2  2 2a+2  0 2a+2  2 2a  0
 0  0  0  2  0  0 2a+2  2  0 2a 2a 2a  0 2a+2  2 2a  2 2a 2a+2 2a+2 2a  0 2a+2
 0  0  0  0  2  0  2 2a+2 2a  0  2 2a+2 2a 2a 2a+2  0  0 2a 2a  0 2a+2 2a 2a
 0  0  0  0  0  2 2a+2  2 2a+2  2 2a+2  2  2 2a  0 2a+2  0  0 2a  0  2  2 2a

generates a code of length 23 over GR(16,4) 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 code over GF(4) with n=92, k=7 and d=52.
This code was found by Heurico 1.16 in 0.718 seconds.