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

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+648x^200+264x^201+576x^203+735x^204+264x^205+444x^208+48x^209+237x^212+318x^216+168x^217+192x^219+153x^220+24x^221+18x^224+3x^228+3x^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 28.7 seconds.