The generator matrix

 1  0  1  1  1  1  1  1  0  1  1  1  1
 0  1  1  a a+1  0 (a+1)X+1  a  1  0 (a+1)X+1 (a+1)X+1 (a+1)X+1
 0  0 (a+1)X  0  0  X  0  X  X  X (a+1)X aX aX
 0  0  0  X  0 (a+1)X (a+1)X (a+1)X  X aX (a+1)X  0  0
 0  0  0  0 (a+1)X  X (a+1)X aX (a+1)X (a+1)X (a+1)X  0  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+126x^28+48x^30+474x^32+384x^33+432x^34+1701x^36+2304x^37+1296x^38+3762x^40+3456x^41+1296x^42+984x^44+99x^48+21x^52

The gray image is a linear code over GF(4) with n=52, k=7 and d=28.
This code was found by Heurico 1.16 in 0.155 seconds.