The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 (a+1)X 1 1 1 1 (a+1)X 1 (a+1)X 1 1 1 1 (a+1)X 1 1 X 1 1 1 1 1 (a+1)X 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 aX 1 aX 1 1 (a+1)X 1 1 1 1 1 1 1 1 aX 1 0 1 0 0 0 (a+1)X 1 (a+1)X+a a+1 (a+1)X+1 1 (a+1)X+a (a+1)X+a+1 (a+1)X+a+1 1 1 a (a+1)X+1 a+1 a 1 aX 1 X+a X+a+1 X+1 1 X (a+1)X+a+1 a 1 aX (a+1)X (a+1)X+a 0 X+a+1 1 0 (a+1)X+1 aX+1 aX+a a+1 aX+a+1 X+a aX (a+1)X+a 0 (a+1)X+a+1 aX 1 (a+1)X+a aX 1 1 1 aX 1 1 0 aX+a X+a aX+a X X X+1 X+a+1 1 X+1 0 0 1 1 a a+1 1 X+1 1 0 a+1 X+a+1 aX a a 1 aX+a a a+1 X a+1 X+1 (a+1)X (a+1)X+1 X+1 (a+1)X (a+1)X+1 1 (a+1)X+a+1 X+a+1 aX+1 X X+a+1 X a X aX+a aX+1 X+a (a+1)X+1 0 (a+1)X+a a+1 (a+1)X+a aX+a+1 aX+1 1 0 (a+1)X+1 X+a+1 (a+1)X+a+1 X+a a+1 (a+1)X+a+1 X+a a+1 aX+1 (a+1)X+a+1 (a+1)X+1 (a+1)X+a+1 a X 0 (a+1)X+a+1 X+a aX+a aX+a+1 a 0 0 0 (a+1)X 0 0 0 aX aX aX (a+1)X X X X X (a+1)X (a+1)X aX (a+1)X X aX X 0 0 (a+1)X 0 (a+1)X X aX 0 0 aX X (a+1)X 0 aX aX aX 0 X X aX aX X aX 0 aX 0 X aX (a+1)X (a+1)X X 0 aX (a+1)X (a+1)X 0 0 0 X X aX X aX X X X 0 0 0 0 X aX (a+1)X X 0 aX X (a+1)X X 0 X (a+1)X aX 0 aX 0 X (a+1)X (a+1)X X (a+1)X aX 0 0 (a+1)X (a+1)X aX X X 0 (a+1)X aX 0 (a+1)X (a+1)X X (a+1)X aX 0 0 aX aX X aX 0 aX (a+1)X (a+1)X aX 0 aX aX aX aX aX X (a+1)X X aX (a+1)X X X 0 (a+1)X generates a code of length 68 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 187. Homogenous weight enumerator: w(x)=1x^0+156x^187+474x^188+384x^189+708x^190+792x^191+1764x^192+936x^193+1728x^194+1236x^195+2871x^196+1884x^197+2844x^198+1848x^199+3564x^200+2376x^201+3480x^202+2604x^203+4497x^204+2352x^205+4044x^206+2448x^207+4641x^208+2184x^209+3696x^210+1932x^211+2952x^212+1356x^213+1572x^214+1032x^215+1374x^216+744x^217+312x^218+216x^219+261x^220+72x^221+48x^222+24x^223+57x^224+21x^228+21x^232+6x^236+15x^240+6x^244+3x^248 The gray image is a linear code over GF(4) with n=272, k=8 and d=187. This code was found by Heurico 1.16 in 19.6 seconds.