The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^3 1 1 X^2 1 1 1 1 X^2 1 1 X X^3+X^2 1 X 1 X^3 X 0 X 0 1 X 1 0 X 0 X 0 X^3 X^3+X X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X 0 X^3+X^2 X X^3+X^2+X X 0 X^3 X^3+X X^2 0 X^2+X X^3+X X^2 X^3+X^2+X X^2+X 0 X^2 X X^3+X 0 X^3 X 0 X X^3+X^2+X X^2 X^3 X^3+X^2 X X^3+X^2+X X^3 X^3+X X^2 X^3+X^2 X^2+X X^3+X^2+X X^3+X^2 X^2 X^3+X^2+X X^2+X X^3+X^2 X^2 X^3+X X 0 X^3 X^2+X X^3+X^2+X 0 X^3 X^2 0 X^3 X^3+X^2 X^3+X X^3+X X^3+X X^3+X 0 X^3 X^3 X^3+X^2 0 X^3+X 0 X^3+X X^2 X^2+X X X^2+X X X^2+X X^2+X 0 0 0 X X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2 X^3+X^2+X X 0 X^3 X^3+X^2+X X^3+X X^2 0 X^3+X X X^2 X^3+X^2+X X X^3+X^2 X^3+X^2 X^2 X^2+X X^3+X^2+X X^3 X^2+X X^3+X X^3 X^3 X^3 X^3+X X^2 X X^2 X^2 X^3+X X^3+X^2+X X^3+X^2 X X^3 X X^2+X X^2 X^2 X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3 X X X^2+X X^2+X X^3 X^3 X^3+X^2+X X^3+X^2+X 0 0 0 X^3+X^2+X X X^3 X^2+X X X^3+X X^3+X^2 X X^2 X^3+X^2 X X^3+X X^3+X X X^3+X X^2+X X X 0 X^2+X X^3 0 0 0 0 0 0 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 0 0 0 0 X^3 0 0 0 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0 X^3 0 0 0 X^3 X^3 generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 84. Homogenous weight enumerator: w(x)=1x^0+72x^84+278x^85+274x^86+354x^87+391x^88+480x^89+499x^90+474x^91+353x^92+320x^93+226x^94+226x^95+70x^96+24x^97+19x^98+14x^99+8x^100+2x^101+6x^102+4x^103+1x^156 The gray image is a linear code over GF(2) with n=720, k=12 and d=336. This code was found by Heurico 1.16 in 1.25 seconds.