The generator matrix

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

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+90x^24+303x^28+465x^32+753x^36+12288x^39+1146x^40+849x^44+378x^48+111x^52

The gray image is a linear code over GF(4) with n=52, k=7 and d=24.
This code was found by Heurico 1.16 in 0.205 seconds.