The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a^2*X 1 a^2*X 1 1 1 0 1 X X 1 1 0 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 a^2*X 1 1 X a^2*X 1 1 1 1 0 a^2*X 1 1 a^2*X 1 1 1 0 1 0 0 0 a^2*X 1 a^2*X+a a^2 a^2*X+1 a^2*X+1 a a^2*X+a a^2 1 a^2*X+a^2 1 1 a^2*X+a^2 a 1 X+a^2 1 1 X+1 X+a^2 a^2*X a*X+a a^2*X+a^2 a*X a^2*X+a a*X+1 a a^2*X a a a*X a*X+a 1 X+a^2 a*X X+1 a a*X X+a 0 X+1 a^2 a*X+a^2 a*X+a 1 a*X+1 a^2*X+a^2 1 a^2*X a^2 a^2 1 a^2*X+a^2 1 1 a*X+1 a^2*X+a^2 1 X X+a^2 a^2*X 0 0 1 1 a a^2 1 X+1 1 a 0 X a^2 a*X+a^2 a^2 a*X+a X+1 a^2 0 X+a a a*X+a^2 X X+a^2 a^2*X+1 a*X+1 1 X+a^2 a^2*X a^2*X X+1 X a*X+a a*X+1 a*X+1 X+a^2 a*X+a^2 a^2*X a*X+a X+a a*X a^2*X+a^2 a a*X+a^2 0 1 X+a^2 a*X+a a^2*X+1 a^2 a*X+1 a^2*X+1 X+a^2 a^2*X+a^2 1 a*X 1 a a*X+a a^2*X+1 a^2*X+1 a*X a a^2 0 X+1 a 0 0 0 a^2*X 0 0 0 X X X a^2*X a*X a^2*X a*X a^2*X a*X a*X X a^2*X a*X X a*X 0 a^2*X a*X a^2*X a^2*X a^2*X a*X a^2*X a^2*X X a^2*X a*X 0 X a*X a^2*X X 0 a*X a*X X a^2*X a*X X 0 a*X a^2*X X 0 0 0 X a*X 0 0 a^2*X a^2*X 0 a^2*X X a^2*X X 0 a*X X 0 0 0 0 X a^2*X a*X X a^2*X a*X a*X X X a*X a*X 0 X a^2*X X a*X 0 a^2*X a^2*X 0 0 a^2*X X a*X a^2*X a*X 0 a*X X X a^2*X a*X 0 a^2*X a*X a*X X X a^2*X X a*X 0 a^2*X a^2*X a*X 0 a*X X 0 a^2*X a^2*X a*X X X a^2*X a^2*X X a^2*X a*X a*X a^2*X 0 a^2*X generates a code of length 67 over F4[X]/(X^2) who´s minimum homogenous weight is 184. Homogenous weight enumerator: w(x)=1x^0+243x^184+156x^185+396x^186+456x^187+1710x^188+792x^189+1008x^190+1296x^191+3489x^192+1872x^193+1536x^194+1704x^195+4329x^196+1944x^197+2256x^198+2460x^199+5637x^200+2340x^201+2904x^202+2676x^203+5949x^204+2664x^205+2208x^206+2184x^207+4362x^208+1608x^209+1392x^210+1296x^211+2190x^212+840x^213+480x^214+204x^215+633x^216+72x^217+108x^218+12x^219+54x^220+21x^224+12x^228+21x^232+9x^236+9x^240+3x^244 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 19.9 seconds.