The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  1  a a+1 (a+1)X (a+1)X+1 (a+1)X+a+1 (a+1)X+a+1 (a+1)X+a+1  0  0  0
 0  0  1 a+1  a  1  1  0  a  0  X  a (a+1)X  0
 0  0  0  X  0  X  0 aX (a+1)X  X aX  X (a+1)X  0
 0  0  0  0  X (a+1)X (a+1)X  0 (a+1)X  X  X (a+1)X  0  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+39x^28+48x^29+36x^30+180x^31+198x^32+468x^33+432x^34+720x^35+1506x^36+3072x^37+1944x^38+4056x^39+6942x^40+8808x^41+3888x^42+8208x^43+9915x^44+8688x^45+2916x^46+2196x^47+735x^48+420x^49+108x^52+12x^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 2.09 seconds.