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 1 X 1 1 1 1 X X 1 1 1 1 X (a+1)X 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 X 1 1 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 (a+1)X+a+1 aX+1 (a+1)X+a+1 0 X+a aX+a+1 (a+1)X 1 1 (a+1)X+1 a 1 aX+a X aX X+1 1 1 1 aX+a aX X+a+1 1 1 aX+a+1 1 (a+1)X X+a aX+a+1 aX+a+1 1 aX X X+a+1 1 0 (a+1)X+1 a+1 (a+1)X+a+1 X+a X+a aX+a+1 aX+1 1 aX+a X+a+1 1 a aX+a+1 (a+1)X 1 1 (a+1)X X aX+1 X+1 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 X aX X aX (a+1)X X X aX aX (a+1)X aX (a+1)X aX aX 0 X 0 X X 0 (a+1)X 0 (a+1)X 0 0 (a+1)X X aX X (a+1)X (a+1)X X aX 0 (a+1)X 0 0 (a+1)X aX aX aX aX (a+1)X (a+1)X X 0 aX 0 0 X aX 0 (a+1)X 0 aX 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 aX 0 (a+1)X X X 0 aX X X X 0 (a+1)X aX (a+1)X X X (a+1)X (a+1)X X X (a+1)X (a+1)X aX (a+1)X (a+1)X aX X (a+1)X 0 (a+1)X 0 (a+1)X X aX 0 X aX X aX X aX aX (a+1)X (a+1)X X 0 (a+1)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 (a+1)X 0 aX X aX X aX 0 aX aX 0 (a+1)X aX aX X aX 0 aX X (a+1)X 0 0 X (a+1)X X 0 X aX aX X X X 0 0 0 0 0 (a+1)X X 0 aX aX X aX aX (a+1)X 0 generates a code of length 81 over F4[X,sigma]/(X^2) who�s minimum homogenous weight is 228. Homogenous weight enumerator: w(x)=1x^0+252x^228+204x^229+168x^230+819x^232+780x^233+348x^234+999x^236+828x^237+540x^238+1242x^240+1104x^241+600x^242+1314x^244+1380x^245+624x^246+1230x^248+1068x^249+540x^250+801x^252+564x^253+204x^254+261x^256+216x^257+48x^258+129x^260+33x^264+24x^268+24x^272+15x^276+6x^280+12x^284+6x^292 The gray image is a linear code over GF(4) with n=324, k=7 and d=228. This code was found by Heurico 1.16 in 2.95 seconds.