The generator matrix

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

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+48x^30+387x^32+384x^33+576x^34+2052x^36+3456x^37+2592x^38+9966x^40+10368x^41+5184x^42+14976x^44+10368x^45+3888x^46+756x^48+276x^52+90x^56

The gray image is a linear code over GF(4) with n=56, k=8 and d=28.
This code was found by Heurico 1.16 in 2.24 seconds.