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 X 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X 0 0 0 0 0 0 0 0 0 aX (a+1)X X aX X X aX aX aX (a+1)X aX aX aX aX X aX 0 X (a+1)X 0 aX X (a+1)X 0 aX aX (a+1)X X 0 aX X X aX X X X (a+1)X X (a+1)X aX (a+1)X X aX (a+1)X X 0 0 0 aX aX aX (a+1)X 0 (a+1)X (a+1)X X 0 (a+1)X 0 (a+1)X 0 0 0 X 0 0 0 0 X X X aX 0 aX (a+1)X (a+1)X 0 aX 0 X X X (a+1)X X 0 0 X (a+1)X (a+1)X 0 aX aX aX X (a+1)X (a+1)X 0 X 0 X aX (a+1)X X aX X (a+1)X X X (a+1)X 0 0 (a+1)X (a+1)X X 0 (a+1)X X aX aX aX 0 (a+1)X aX (a+1)X X X 0 aX (a+1)X (a+1)X X X 0 0 0 0 X 0 0 X (a+1)X aX aX aX aX 0 X X (a+1)X X (a+1)X X aX 0 aX 0 0 aX aX 0 aX 0 aX 0 0 X aX (a+1)X X X X X 0 aX (a+1)X 0 aX 0 aX aX 0 aX aX X (a+1)X 0 aX 0 X aX X aX X 0 (a+1)X aX (a+1)X 0 X aX X 0 (a+1)X aX 0 0 0 0 0 X 0 (a+1)X 0 X aX (a+1)X aX (a+1)X (a+1)X 0 X X 0 0 0 (a+1)X X X (a+1)X aX aX 0 (a+1)X (a+1)X (a+1)X X 0 X (a+1)X (a+1)X (a+1)X aX X aX aX (a+1)X aX (a+1)X X 0 0 aX aX X aX 0 aX aX (a+1)X (a+1)X X X aX (a+1)X aX aX X (a+1)X aX X aX aX 0 X (a+1)X X 0 0 0 0 0 0 X X X (a+1)X X X 0 (a+1)X (a+1)X X X aX (a+1)X 0 aX aX aX (a+1)X (a+1)X X aX (a+1)X 0 0 X (a+1)X 0 X X X X aX X 0 aX aX 0 X (a+1)X X (a+1)X (a+1)X 0 X X 0 X X (a+1)X X (a+1)X 0 (a+1)X (a+1)X aX 0 0 aX 0 X (a+1)X (a+1)X (a+1)X 0 aX X aX generates a code of length 72 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 192. Homogenous weight enumerator: w(x)=1x^0+96x^192+276x^196+417x^200+348x^204+495x^208+768x^210+327x^212+4608x^214+390x^216+6912x^218+423x^220+309x^224+258x^228+267x^232+171x^236+126x^240+84x^244+60x^248+30x^252+9x^256+3x^260+3x^264+3x^280 The gray image is a linear code over GF(4) with n=288, k=7 and d=192. This code was found by Heurico 1.16 in 3.34 seconds.