The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 (a+1)X 1 0 1 1 1 (a+1)X aX 1 1 1 1 1 1 1 1 1 1 0 X 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 X (a+1)X 1 1 1 1 1 1 1 aX 0 0 1 X 1 1 1 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 (a+1)X+a+1 1 (a+1)X+a+1 1 (a+1)X+1 a+1 a 1 1 a+1 (a+1)X+a+1 0 X+1 a 1 X X+a+1 X aX+a 1 1 (a+1)X+1 aX+1 (a+1)X aX aX+a+1 X+a a X+a+1 1 aX+a 1 1 aX+1 (a+1)X+a 1 1 1 0 (a+1)X+a+1 (a+1)X+1 1 (a+1)X+a+1 aX (a+1)X+1 (a+1)X 1 (a+1)X a 1 X+a X+a X+1 X+1 0 0 1 1 a a+1 1 X+1 1 0 a+1 X+a+1 a aX+a X+1 aX a a a+1 X X+a+1 0 (a+1)X+a X+1 (a+1)X+a X (a+1)X+a+1 (a+1)X+1 (a+1)X+a+1 aX+a+1 (a+1)X X+a (a+1)X+a X+a+1 (a+1)X+a aX+a aX+a aX+1 aX X X+1 X (a+1)X aX+a+1 aX+1 a+1 X+1 aX+1 (a+1)X+a+1 (a+1)X+a (a+1)X aX+a (a+1)X+1 X+a+1 aX a+1 X+a (a+1)X+1 1 aX+a+1 1 X X+1 (a+1)X aX+a+1 X a+1 0 0 0 (a+1)X 0 0 0 aX aX aX (a+1)X X (a+1)X X (a+1)X X X aX (a+1)X X aX 0 X (a+1)X aX 0 aX 0 X 0 X (a+1)X 0 0 (a+1)X aX X aX 0 X 0 0 aX aX X aX (a+1)X 0 X X aX (a+1)X (a+1)X aX (a+1)X aX (a+1)X (a+1)X 0 X aX (a+1)X X aX (a+1)X 0 X 0 0 0 0 X aX (a+1)X X 0 aX X (a+1)X aX 0 (a+1)X X X 0 aX 0 X (a+1)X aX (a+1)X X aX aX X (a+1)X 0 aX X X (a+1)X aX X aX 0 X aX X (a+1)X X (a+1)X aX (a+1)X aX aX 0 aX (a+1)X aX 0 0 0 0 0 X aX aX 0 X 0 X aX 0 0 generates a code of length 67 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 184. Homogenous weight enumerator: w(x)=1x^0+324x^184+288x^185+156x^186+384x^187+1974x^188+972x^189+576x^190+1224x^191+3849x^192+1452x^193+924x^194+1848x^195+5694x^196+1980x^197+960x^198+2364x^199+7080x^200+2568x^201+1320x^202+2736x^203+7002x^204+2232x^205+1152x^206+2592x^207+5424x^208+1884x^209+732x^210+888x^211+2712x^212+732x^213+288x^214+252x^215+609x^216+144x^217+36x^218+66x^220+36x^221+24x^224+18x^228+24x^232+6x^236+6x^240+3x^248 The gray image is a linear code over GF(4) with n=268, k=8 and d=184. This code was found by Heurico 1.16 in 19.4 seconds.