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 X 1 1 1 X X X X X 1 X 1 1 1 1 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+40x^58+124x^60+201x^62+233x^64+265x^66+308x^68+494x^70+983x^72+1434x^74+8192x^75+1450x^76+1000x^78+524x^80+340x^82+242x^84+194x^86+168x^88+94x^90+50x^92+31x^94+10x^96+3x^98+2x^100+1x^136 The gray image is a linear code over GF(2) with n=300, k=14 and d=116. This code was found by Heurico 1.16 in 32.7 seconds.