The generator matrix

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

generates a code of length 68 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+492x^196+1662x^200+603x^204+516x^208+384x^212+372x^216+51x^220+6x^224+6x^228+3x^240

The gray image is a linear code over GF(4) with n=272, k=6 and d=196.
This code was found by Heurico 1.16 in 0.131 seconds.