The generator matrix

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

generates a code of length 14 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+48x^36+432x^37+144x^38+480x^39+222x^40+864x^41+96x^42+360x^44+1008x^45+144x^46+288x^47+9x^48

The gray image is a linear code over GF(4) with n=56, k=6 and d=36.
This code was found by Heurico 1.16 in -3.62e-008 seconds.