The generator matrix 1 0 1 1 X^2 1 1 1 X^2+X 1 1 0 X^3+X 1 1 1 1 X^2 1 1 X^3 1 1 X^3 1 1 X 1 1 X^3+X^2+X 1 X^3+X 1 0 1 1 1 X^2+X 1 1 X^2+X 0 1 X^3+X 1 1 1 1 1 1 1 1 1 1 0 1 X X^3+X^2 1 1 X^2+X 1 1 X^2 1 1 1 1 1 1 X^2+X X^3+X^2+X X X^3 X^2 X 1 1 1 1 1 1 X^3 X^3+X^2+X 1 1 X^3+X X^3+X 1 1 X^3 X^2 1 1 0 1 1 X^2+X 1 X^2+X+1 X^2 X^3+1 1 X+1 X^3+X^2+X 1 1 0 X^3+X^2+1 X^3 X^3+1 1 X X+1 1 X^2+X X^3+X+1 1 X^2 X^2+1 1 X^3+X^2+X+1 X^3+X^2 1 1 1 X 1 X^3+X X+1 X^3+X^2 1 X^3+X X^3+X 1 1 X^3+1 1 X^2 X^3+X^2+X+1 X^3+X^2+1 X^3+X^2+X+1 X^3+X^2+X+1 X^3+1 X^2+X+1 X^3+1 X^3 X X^3+X^2 X^3 X^2+X 1 X^3+1 X^3 1 X^3+X^2+X X^3+X+1 1 0 X^2 X^3+X^2+X+1 X^3+X^2 X X^3+X^2 1 1 1 1 X X^3+X X^3 X^2+X+1 X^3+X^2+1 X^3+X X^3+X^2+1 X^2+X 1 1 X^3+1 X^2+X+1 1 1 X X^3+X+1 1 1 1 0 0 0 X 0 X^3+X X X^3+X X^3 0 X^3 X^3+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2+X X^2 X^2+X X^3+X X^2+X X^2 X^2 X^2 X^2+X X X^3+X^2 X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^3 X^3 X^3+X 0 X X X^3+X^2 X^2 X^3+X^2 X^2+X X^2+X X X^2+X 0 0 X^3+X 0 X^3 X X X^3+X X X^2 X^2+X 0 X^3+X^2 X^3+X X^3+X 0 X^2+X X^2+X 0 X^2+X X^3+X^2 X^3 0 X^2 X^3 X^3+X^2+X X^2 X X^3+X^2 X^3+X^2+X X^3 X^3+X^2+X 0 X^3+X^2 X^3 X^3+X X^3+X^2 X^3+X^2 X^3+X 0 X^3+X^2 X^3+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^2 X^2 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 0 generates a code of length 94 over Z2[X]/(X^4) who´s minimum homogenous weight is 89. Homogenous weight enumerator: w(x)=1x^0+98x^89+419x^90+524x^91+500x^92+444x^93+469x^94+412x^95+354x^96+274x^97+190x^98+196x^99+136x^100+24x^101+18x^102+8x^103+8x^104+6x^106+4x^107+8x^108+1x^118+1x^120+1x^122 The gray image is a linear code over GF(2) with n=752, k=12 and d=356. This code was found by Heurico 1.16 in 1.27 seconds.