The generator matrix

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

generates a code of length 19 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+324x^51+132x^52+384x^53+192x^54+732x^55+222x^56+384x^57+96x^58+444x^59+270x^60+384x^61+96x^62+420x^63+9x^64+6x^68

The gray image is a linear code over GF(4) with n=76, k=6 and d=51.
This code was found by Heurico 1.16 in 0.078 seconds.