The generator matrix

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

generates a code of length 14 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+168x^28+387x^32+1284x^36+5358x^40+8064x^44+756x^48+276x^52+90x^56

The gray image is a linear code over GF(4) with n=56, k=7 and d=28.
This code was found by Heurico 1.16 in 0.294 seconds.