The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 X 1 X 1 1 0 1 0 X 1 0 1 1 X 0 1 1 0 1 1 1 X 0 X X^2 X 1 X X 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 X^2+X 0 X^2+X X X^2+X X^2+X X X^2+X X^2 0 X X^2+X X X^2+X 0 X 0 X^2 X^2+X X X^2+X X^2+X X X^2 X X X^2+X X X^2+X X^2 X^2+X X^2+X X^2 X^2+X 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 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 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 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 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 0 X^2 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 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 generates a code of length 48 over Z2[X]/(X^3) who´s minimum homogenous weight is 36. Homogenous weight enumerator: w(x)=1x^0+156x^36+66x^38+546x^40+850x^42+1845x^44+2964x^46+3682x^48+2564x^50+2245x^52+682x^54+577x^56+42x^58+135x^60+24x^64+3x^68+1x^72+1x^80 The gray image is a linear code over GF(2) with n=192, k=14 and d=72. This code was found by Heurico 1.16 in 15.4 seconds.