The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 X 1 1 1 1 1 X 1 1
0 X 0 0 0 0 X X X aX 0 X (a+1)X aX (a+1)X aX X X aX 0 (a+1)X aX X aX 0 X 0 (a+1)X aX X (a+1)X aX 0 0 aX aX X (a+1)X X (a+1)X (a+1)X 0 (a+1)X aX aX aX X X 0 aX 0 0 0 aX aX X 0 (a+1)X aX X aX X (a+1)X (a+1)X aX aX 0 aX 0 X X X 0 X X (a+1)X 0
0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX aX 0 aX (a+1)X aX (a+1)X (a+1)X 0 X (a+1)X 0 (a+1)X 0 aX aX aX aX (a+1)X 0 (a+1)X (a+1)X 0 0 (a+1)X X X 0 aX 0 X aX X X X aX X 0 0 aX aX aX X X X X 0 X X (a+1)X X 0 aX X aX (a+1)X X (a+1)X X X aX aX X X X
0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X 0 X (a+1)X X X (a+1)X (a+1)X (a+1)X aX 0 (a+1)X (a+1)X 0 X aX 0 (a+1)X 0 aX X X aX 0 aX 0 X (a+1)X 0 (a+1)X 0 aX X aX X aX aX (a+1)X X X (a+1)X (a+1)X 0 aX 0 X X aX 0 X (a+1)X 0 aX X X (a+1)X X aX X 0 (a+1)X X aX 0 aX
0 0 0 0 X X X (a+1)X X X X aX 0 0 0 aX X aX (a+1)X (a+1)X aX 0 aX X aX aX 0 0 (a+1)X (a+1)X (a+1)X aX X 0 0 X aX aX X 0 aX X (a+1)X (a+1)X X (a+1)X (a+1)X (a+1)X X (a+1)X aX aX (a+1)X 0 (a+1)X (a+1)X (a+1)X 0 X X 0 X X aX aX aX (a+1)X 0 0 X 0 0 aX 0 aX X X
generates a code of length 77 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 216.
Homogenous weight enumerator: w(x)=1x^0+90x^216+219x^220+48x^222+159x^224+432x^226+135x^228+1296x^230+87x^232+1296x^234+84x^236+69x^240+36x^244+24x^248+30x^252+39x^256+15x^260+12x^264+9x^268+6x^272+6x^280+3x^296
The gray image is a linear code over GF(4) with n=308, k=6 and d=216.
This code was found by Heurico 1.16 in 0.29 seconds.