The generator matrix

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

generates a code of length 13 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+168x^32+192x^33+222x^36+1152x^37+366x^40+1728x^41+228x^44+33x^48+6x^52

The gray image is a linear code over GF(4) with n=52, k=6 and d=32.
This code was found by Heurico 1.16 in 0.0121 seconds.