The generator matrix
1 0 1 1 1 1 1 1 1 1 1 1 1
0 1 1 a 0 (a+1)X+1 a X (a+1)X+1 X+a X 1 X+a
0 0 (a+1)X X X 0 (a+1)X aX aX 0 (a+1)X X aX
generates a code of length 13 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 35.
Homogenous weight enumerator: w(x)=1x^0+216x^35+69x^36+336x^39+180x^40+216x^43+3x^48+3x^52
The gray image is a linear code over GF(4) with n=52, k=5 and d=35.
This code was found by Heurico 1.16 in 0.078 seconds.