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.