The generator matrix

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

generates a code of length 69 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 196.

Homogenous weight enumerator: w(x)=1x^0+1428x^196+2844x^200+3849x^204+3078x^208+2208x^212+1764x^216+852x^220+345x^224+6x^228+3x^236+6x^244

The gray image is a linear code over GF(4) with n=276, k=7 and d=196.
This code was found by Heurico 1.16 in 6.77 seconds.