The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 X 1 1 a*X 1 1 1 1 1 1 1 1 1 0 1 1 a^2*X 1 1 1 a^2*X 1 1 1 X 1 1 1 1 X 1 0 1 1 X 1 a^2*X X 1 a^2*X 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 a a^2 0 a^2*X+1 a^2*X+a^2 a 1 0 a^2*X+1 a 1 a^2*X+a^2 X a^2*X+a^2 X+a a^2*X+1 1 a^2*X+a^2 a 1 1 a^2*X+a a^2 0 a a*X+1 0 a*X+a^2 a^2*X 1 a^2*X+a^2 a^2*X+a 1 a^2 a^2*X+1 X+a^2 1 X+a a*X+1 a^2*X+1 1 a*X a^2 a^2*X+a a*X 1 a^2 1 X 1 1 a^2*X 1 1 a^2*X+a^2 1 1 a*X+a X a*X+a^2 X+1 a^2*X a^2*X+a a^2*X+1 a^2*X+a 1 X+a a*X+1 a*X a*X+a a^2*X a^2 a 0 X+a^2 a^2*X+a^2 a^2*X 1 0 0 a^2*X 0 0 0 X X X X X X a^2*X a^2*X a*X X a*X a^2*X a^2*X 0 a^2*X a^2*X a*X X 0 0 a*X a*X a*X 0 a*X X 0 X X X a^2*X a*X a^2*X a*X 0 0 a^2*X a*X 0 a*X 0 0 X a*X a*X a*X a^2*X a^2*X a^2*X a*X 0 a^2*X X 0 a*X X a*X a*X X X X a^2*X X X X a*X a*X X 0 0 a*X X X a*X X 0 0 0 X 0 X a^2*X 0 X a^2*X X 0 a*X a^2*X 0 a^2*X 0 0 a*X a*X X X a^2*X 0 a^2*X a*X a*X 0 a*X X 0 a*X a^2*X a*X a^2*X a*X X a*X a*X a*X a^2*X 0 a*X a^2*X 0 X X a^2*X 0 a^2*X 0 a*X a^2*X a^2*X X 0 a*X a^2*X X 0 X a*X X a^2*X X a*X a*X a*X X a^2*X a*X X X 0 0 X a*X a*X 0 0 a*X 0 0 0 0 a^2*X a^2*X X a^2*X a*X 0 a^2*X X X a*X X a*X a*X X a^2*X a^2*X 0 a^2*X a^2*X a*X 0 a^2*X a^2*X 0 a*X a*X a^2*X 0 a*X X 0 X X 0 a^2*X a^2*X a*X a^2*X a*X 0 a*X 0 a*X a^2*X 0 0 X X X 0 X 0 a*X a*X a*X X X X a*X a^2*X 0 X 0 0 X X a^2*X X 0 a*X 0 a^2*X a*X a^2*X 0 a*X 0 generates a code of length 81 over F4[X]/(X^2) who´s minimum homogenous weight is 228. Homogenous weight enumerator: w(x)=1x^0+279x^228+144x^229+264x^231+1047x^232+372x^233+492x^235+1410x^236+432x^237+396x^239+2046x^240+564x^241+636x^243+1767x^244+636x^245+624x^247+1860x^248+396x^249+468x^251+1272x^252+408x^253+156x^255+375x^256+108x^257+36x^259+84x^260+12x^261+24x^264+9x^268+18x^272+15x^276+15x^280+3x^284+6x^288+9x^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 2.03 seconds.