The generator matrix

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

generates a code of length 13 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+84x^28+165x^32+180x^36+3072x^39+240x^40+204x^44+138x^48+12x^52

The gray image is a linear code over GF(4) with n=52, k=6 and d=28.
This code was found by Heurico 1.16 in 0.0206 seconds.