The generator matrix

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

generates a code of length 65 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 179.

Homogenous weight enumerator: w(x)=1x^0+708x^179+615x^180+3348x^183+1257x^184+6192x^187+2274x^188+8400x^191+2835x^192+10260x^195+3831x^196+10260x^199+2904x^200+6984x^203+1827x^204+2568x^207+624x^208+432x^211+117x^212+9x^216+48x^220+12x^224+21x^228+6x^232+3x^236

The gray image is a linear code over GF(4) with n=260, k=8 and d=179.
This code was found by Heurico 1.16 in 97 seconds.