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

generates a code of length 67 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 193.

Homogenous weight enumerator: w(x)=1x^0+144x^193+168x^194+792x^195+90x^196+192x^197+288x^198+792x^199+78x^200+144x^201+108x^202+144x^203+30x^204+144x^205+12x^206+24x^208+96x^209+156x^210+504x^211+18x^212+48x^213+36x^214+72x^215+6x^216+6x^220+3x^224

The gray image is a linear code over GF(4) with n=268, k=6 and d=193.
This code was found by Heurico 1.16 in 72.2 seconds.