The generator matrix

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

generates a code of length 14 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+153x^32+192x^33+336x^36+1728x^37+1344x^40+5184x^41+1920x^44+5184x^45+270x^48+48x^52+24x^56

The gray image is a linear code over GF(4) with n=56, k=7 and d=32.
This code was found by Heurico 1.16 in 14.9 seconds.