The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 1 1 X 1 0 X aX 1 1 1 1 1 1 1 1 1 1 1 X 1 1 0 (a+1)X 1 1 1 1 1 1 1 1 (a+1)X 1 1 1 aX 1 X aX (a+1)X 1 1 1 1 aX 1 1 1 1 1 1 1 1 X 0 0 0 1 1 1 1 1 1 1 0 1 0 0 (a+1)X 0 (a+1)X 1 (a+1)X+a (a+1)X+1 aX+1 aX+1 aX+a+1 a aX a+1 (a+1)X 1 1 (a+1)X+a+1 (a+1)X+1 1 aX 0 X+a+1 X+a 1 aX+a+1 (a+1)X+a (a+1)X+a+1 1 aX a 1 1 aX (a+1)X+a X+a+1 aX+a X+a+1 X+a+1 (a+1)X aX+1 1 (a+1)X+a X aX+a 1 (a+1)X+1 1 1 1 aX+a X+a+1 aX+a a aX (a+1)X 1 aX aX+1 (a+1)X+a (a+1)X+a+1 (a+1)X (a+1)X+a+1 (a+1)X 1 (a+1)X 1 (a+1)X (a+1)X+1 aX+a+1 (a+1)X+1 aX+a+1 X+a+1 X+a 0 0 1 0 X aX 0 (a+1)X (a+1)X aX aX (a+1)X X (a+1)X+a+1 1 (a+1)X+1 1 a aX+a+1 X+a+1 X+1 X+a aX+1 X+a+1 X+a+1 a+1 (a+1)X+a+1 aX+a aX+a+1 (a+1)X+a a+1 X+a+1 X+a (a+1)X+1 (a+1)X+1 aX+a+1 (a+1)X+1 (a+1)X+a+1 1 aX+a (a+1)X+a 1 (a+1)X+a a aX+1 aX+a+1 X (a+1)X+a a 0 a+1 X X+a aX X+a+1 X 1 X+a aX+a+1 (a+1)X+a (a+1)X+1 1 aX+1 a+1 aX+a+1 1 (a+1)X+1 1 X X+a X+a+1 1 0 X+1 0 (a+1)X+a 0 0 0 1 (a+1)X+1 a a+1 (a+1)X+a+1 X+a+1 aX+a (a+1)X aX+1 X+a (a+1)X+a X+a+1 aX+a+1 (a+1)X+a 1 X+a aX+a+1 X X+a+1 X+1 X+1 a (a+1)X X+a aX+1 (a+1)X+1 X a+1 (a+1)X+a+1 0 (a+1)X+1 aX (a+1)X+a a 0 (a+1)X aX+a+1 X+a aX aX a+1 a+1 0 X a X+1 X+1 (a+1)X (a+1)X+a (a+1)X+a+1 (a+1)X+a+1 X+a+1 aX+a X+1 a (a+1)X 0 a aX+1 aX+1 X+a X+a (a+1)X+1 aX+1 (a+1)X X+a (a+1)X+a+1 1 a+1 (a+1)X+a a aX+a+1 aX+1 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+354x^212+744x^213+768x^214+888x^215+1464x^216+1704x^217+2208x^218+1644x^219+2271x^220+2592x^221+2472x^222+2088x^223+3060x^224+3096x^225+3036x^226+2088x^227+3369x^228+3492x^229+3084x^230+2136x^231+3240x^232+3396x^233+2592x^234+1920x^235+2697x^236+2100x^237+1740x^238+1020x^239+1065x^240+1068x^241+840x^242+444x^243+357x^244+240x^245+144x^246+60x^247+42x^248+12x^250 The gray image is a linear code over GF(4) with n=304, k=8 and d=212. This code was found by Heurico 1.16 in 24.5 seconds.