The generator matrix

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

generates a code of length 67 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 194.

Homogenous weight enumerator: w(x)=1x^0+612x^194+444x^195+120x^196+612x^198+492x^199+54x^200+480x^202+276x^203+180x^206+168x^207+39x^208+240x^210+36x^211+24x^212+120x^214+108x^215+15x^216+60x^218+12x^219+3x^232

The gray image is a linear code over GF(4) with n=268, k=6 and d=194.
This code was found by Heurico 1.16 in 0.11 seconds.