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 0 1 1 a*X 1 1 1 1 a^2*X 1 1 1 1 a^2*X 1 1 1 1 1 X 1 1 a*X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 a*X 1 1 X 1 1 a^2*X 1 1 1 1 1 1 1 1 1 1 1 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 0 a a^2 a^2*X+1 a*X+1 1 a^2*X a*X+1 1 a*X+a 0 a*X+a^2 a*X+1 1 a^2*X+a a*X+1 a*X+1 a*X+a^2 1 a*X+a^2 a*X a*X+a^2 a*X+a^2 X 1 a^2*X+a^2 X+1 1 a^2*X a*X a*X+1 a^2*X+a a^2 a a^2*X+a^2 X+1 1 a^2*X+a a*X a*X a*X+a^2 0 1 X X 1 0 a^2*X+1 1 0 a*X+a a*X+1 a*X+a^2 a^2*X+1 a*X+a^2 a^2*X+a^2 a^2*X+a a a^2*X+1 0 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 a^2*X a*X 0 a*X X X a^2*X a*X a^2*X 0 a^2*X a*X 0 a*X a*X X a*X X a^2*X a^2*X a*X a*X 0 0 0 X X X X X a*X a*X 0 a*X 0 a*X 0 0 0 X a*X 0 0 a*X a*X a*X X X X a^2*X 0 a^2*X X a*X a*X X X X 0 0 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 a^2*X 0 a*X a*X 0 a^2*X X X a*X X X 0 X a^2*X X 0 X X X a^2*X 0 a^2*X 0 0 a*X a*X X 0 a^2*X 0 0 a^2*X a*X a*X a^2*X a*X X a*X a*X X a^2*X 0 a*X a^2*X a*X X 0 X a*X 0 a^2*X X X a*X a*X a*X a*X a^2*X 0 0 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 X 0 a^2*X 0 a^2*X a^2*X a*X X X a*X X a^2*X X 0 a*X a*X 0 a^2*X a*X 0 X 0 a*X a^2*X X a*X X 0 a^2*X 0 0 a*X 0 X 0 a*X a*X a*X a^2*X X a*X X a*X X 0 X a*X 0 a^2*X a*X a^2*X 0 a*X X a^2*X X a*X 0 X X generates a code of length 83 over F4[X]/(X^2) who�s minimum homogenous weight is 232. Homogenous weight enumerator: w(x)=1x^0+117x^232+468x^235+339x^236+1368x^239+600x^240+1824x^243+642x^244+2316x^247+645x^248+2424x^251+513x^252+2400x^255+615x^256+1104x^259+312x^260+348x^263+153x^264+36x^267+60x^268+12x^272+33x^276+15x^280+12x^284+12x^288+9x^292+6x^296 The gray image is a linear code over GF(4) with n=332, k=7 and d=232. This code was found by Heurico 1.16 in 1.93 seconds.