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
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 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 0
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
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 0
generates a code of length 76 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 212.
Homogenous weight enumerator: w(x)=1x^0+54x^212+180x^216+48x^219+216x^220+432x^223+111x^224+1296x^227+105x^228+1296x^231+102x^232+66x^236+33x^240+27x^244+36x^248+30x^252+21x^256+15x^260+12x^264+6x^268+6x^276+3x^292
The gray image is a linear code over GF(4) with n=304, k=6 and d=212.
This code was found by Heurico 1.16 in 0.281 seconds.