The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 X 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 (a+1)X 1 X 1 1 X X 1 1 1 1 1 (a+1)X 1 1 1 1 1 aX X 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 (a+1)X 1 (a+1)X 1 1 0 1 1 a a+1 0 (a+1)X+1 (a+1)X+a+1 a 1 0 (a+1)X+1 (a+1)X+a+1 1 a X (a+1)X+a+1 1 (a+1)X+1 a aX+a+1 0 aX+1 1 a aX+a+1 a+1 aX+1 aX X+a a+1 0 1 1 (a+1)X+a+1 1 aX+a aX+a 1 1 (a+1)X+a+1 (a+1)X+a aX (a+1)X+a X+1 1 (a+1)X+a+1 aX+1 (a+1)X X (a+1)X+a+1 1 1 aX+a+1 X+1 aX+a+1 aX+1 X+1 X+a X+1 aX+a a aX 1 a+1 a+1 aX aX (a+1)X+a 1 aX+1 1 X+1 1 a 0 0 0 (a+1)X 0 0 0 X aX X X X (a+1)X (a+1)X aX aX aX 0 0 X aX (a+1)X aX (a+1)X (a+1)X (a+1)X aX aX X X aX (a+1)X X X aX (a+1)X aX (a+1)X (a+1)X (a+1)X aX X aX aX X 0 aX X aX aX (a+1)X (a+1)X 0 X aX X (a+1)X X aX (a+1)X aX (a+1)X aX (a+1)X X X 0 0 aX 0 X aX (a+1)X 0 X X X 0 0 0 X 0 X (a+1)X (a+1)X X (a+1)X 0 (a+1)X X X 0 X (a+1)X 0 (a+1)X 0 0 X (a+1)X (a+1)X X aX (a+1)X (a+1)X X (a+1)X (a+1)X 0 0 X (a+1)X (a+1)X X 0 (a+1)X (a+1)X aX (a+1)X X X (a+1)X (a+1)X (a+1)X X 0 0 aX X X 0 aX X X X 0 0 X aX X 0 0 aX 0 aX (a+1)X (a+1)X X X aX 0 0 X 0 0 0 0 (a+1)X (a+1)X (a+1)X (a+1)X 0 aX X aX 0 aX (a+1)X X X (a+1)X X aX X (a+1)X 0 (a+1)X aX X 0 0 X aX (a+1)X (a+1)X aX (a+1)X X aX X 0 aX (a+1)X 0 (a+1)X aX X aX 0 (a+1)X 0 0 (a+1)X X 0 0 (a+1)X X (a+1)X aX X aX aX 0 0 X (a+1)X (a+1)X 0 (a+1)X (a+1)X X 0 aX 0 X 0 aX aX 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+141x^212+60x^214+336x^215+651x^216+336x^218+732x^219+948x^220+528x^222+1032x^223+1131x^224+528x^226+1116x^227+1512x^228+732x^230+1440x^231+1179x^232+528x^234+948x^235+963x^236+312x^238+456x^239+429x^240+48x^242+84x^243+99x^244+42x^248+9x^252+12x^256+18x^260+18x^264+6x^268+9x^272 The gray image is a linear code over GF(4) with n=304, k=7 and d=212. This code was found by Heurico 1.16 in 1.75 seconds.