The generator matrix

 1  0  1  1  1  1  1  1  1  0  0  1  1  1  1  1  1  0  0  1  1  1  1
 0  1  1  a a+1  0 (a+1)X+1  a (a+1)X+a+1  1  1  0 (a+1)X+a+1 (a+1)X+1  a  0  a  1  1  0 (a+1)X+1  a  X
 0  0 (a+1)X  0  0  0  0  X aX  X  X  X (a+1)X (a+1)X aX  X  0  X  0  0 (a+1)X  X (a+1)X
 0  0  0  X  0  0  X (a+1)X (a+1)X aX (a+1)X (a+1)X (a+1)X (a+1)X  0  0 aX (a+1)X aX  0  X  0 (a+1)X
 0  0  0  0 (a+1)X  0 aX  0  X  X (a+1)X aX  X aX aX  0 aX  0  X aX aX  X (a+1)X
 0  0  0  0  0  X aX  X aX aX aX  0  0  0  0  X (a+1)X (a+1)X  X  X (a+1)X  X  X

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

Homogenous weight enumerator: w(x)=1x^0+117x^52+24x^54+60x^55+351x^56+48x^57+360x^58+420x^59+645x^60+576x^61+2160x^62+1560x^63+2283x^64+2592x^65+6480x^66+3720x^67+5841x^68+5184x^69+9720x^70+4332x^71+5892x^72+3888x^73+5832x^74+2196x^75+651x^76+432x^80+138x^84+33x^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 5.59 seconds.