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

generates a code of length 69 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 200.

Homogenous weight enumerator: w(x)=1x^0+672x^200+492x^202+888x^204+336x^206+639x^208+132x^210+276x^212+24x^214+282x^216+108x^218+60x^220+24x^222+120x^224+36x^226+6x^240

The gray image is a linear code over GF(4) with n=276, k=6 and d=200.
This code was found by Heurico 1.16 in 0.109 seconds.