The generator matrix

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

generates a code of length 13 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+384x^31+366x^32+384x^33+1152x^35+975x^36+2304x^37+2688x^39+2106x^40+3456x^41+1920x^43+606x^44+39x^48+3x^52

The gray image is a linear code over GF(4) with n=52, k=7 and d=31.
This code was found by Heurico 1.16 in 29.3 seconds.