The generator matrix

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

generates a code of length 13 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+432x^34+504x^35+69x^36+864x^38+528x^39+180x^40+1008x^42+504x^43+3x^48+3x^52

The gray image is a linear code over GF(4) with n=52, k=6 and d=34.
This code was found by Heurico 1.16 in 0.015 seconds.