The generator matrix 1 0 1 1 1 X^2 1 1 0 0 1 1 1 X^2 1 1 1 X^2 1 1 0 1 X^2 1 1 1 X^2+X 1 X^2+X 1 1 1 X 1 X^2 X^2+X 1 1 X 1 0 1 1 1 1 1 1 1 1 X^2 X^2+X 1 1 1 X^2 1 1 1 1 0 1 1 X^2+X X^2 0 1 1 1 X^2 X^2+X X 0 1 1 1 1 X^2+X X 1 0 1 X^2 X 0 1 1 0 1 1 X^2 X+1 1 1 0 X+1 1 1 0 0 X^2+1 1 X^2+1 0 1 X^2 1 X+1 X^2+X+1 X^2 1 X^2+X+1 1 X^2+X X+1 X 1 X^2+1 1 1 X^2+X+1 X^2+1 1 X 1 X^2+X X 1 0 X^2+1 X^2+X+1 0 X^2+1 1 1 X^2+X X^2+X X^2+1 1 X^2+X+1 X^2+X X+1 X^2+X 1 X^2+1 X+1 1 1 1 X^2+1 0 X^2 1 1 1 1 X X^2 1 0 1 1 X+1 1 0 1 X^2 0 0 X 0 0 0 0 0 0 0 0 X^2 X^2 X X X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X X X^2 X^2 X^2+X X^2+X X^2 X X^2 X X X^2 0 X^2+X X^2+X X X 0 X^2 0 0 X X^2+X X 0 X 0 X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X 0 X^2 X^2 X^2 0 X^2 X^2+X X^2+X X^2 X^2+X 0 X^2 X^2+X 0 X X^2+X X^2+X 0 0 0 0 X^2+X X^2 0 X^2+X X^2 0 0 0 X 0 0 X^2 X^2 X^2+X X^2+X X^2+X X X X X^2 X X X^2 0 0 0 X^2+X X^2+X X^2+X X^2 X^2+X X^2+X X^2 0 X^2 X^2+X X^2 X^2+X 0 0 0 X^2+X 0 X^2 X 0 X^2+X 0 X^2+X X X^2+X 0 X X^2 X X^2 X^2+X X X^2 X^2+X 0 X^2+X X 0 X^2+X X^2 0 X^2 X^2 X^2+X X^2 X X^2 X^2 X^2 X X^2 X 0 X X^2+X X^2 X^2+X X^2 X^2 X X X^2+X 0 0 0 0 X X^2+X X^2+X 0 X X^2 X X^2+X X^2 X X X^2 X X^2+X X 0 X^2 X 0 0 X^2+X X^2+X X^2 0 X^2+X X^2+X 0 X^2 X^2+X 0 X^2 X^2+X X^2 X^2 X^2 0 X X^2+X X^2 X^2+X 0 X^2 X^2+X X X^2+X X^2+X 0 X^2 X X^2+X X^2 X^2+X 0 X X^2+X 0 X^2 0 X^2+X 0 X X X^2+X X X^2+X X X^2+X 0 0 X^2 0 0 X^2+X X^2 X^2 X^2 X^2 X X^2 generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 76. Homogenous weight enumerator: w(x)=1x^0+238x^76+100x^77+404x^78+160x^79+479x^80+188x^81+514x^82+128x^83+473x^84+188x^85+368x^86+160x^87+329x^88+100x^89+144x^90+38x^92+24x^94+36x^96+14x^98+3x^100+4x^102+1x^104+2x^112 The gray image is a linear code over GF(2) with n=332, k=12 and d=152. This code was found by Heurico 1.16 in 1.4 seconds.