The generator matrix

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

generates a code of length 13 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+117x^24+48x^27+276x^28+192x^30+576x^31+444x^32+2304x^33+1728x^34+2592x^35+750x^36+13824x^37+5184x^38+5184x^39+1155x^40+20736x^41+5184x^42+3888x^43+888x^44+363x^48+102x^52

The gray image is a linear code over GF(4) with n=52, k=8 and d=24.
This code was found by Heurico 1.16 in 1.74 seconds.