The generator matrix

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

generates a code of length 13 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+303x^28+672x^30+1221x^32+6048x^34+5679x^36+18144x^38+12072x^40+18144x^42+3117x^44+114x^48+21x^52

The gray image is a linear code over GF(4) with n=52, k=8 and d=28.
This code was found by Heurico 1.16 in 11.5 seconds.