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 X 0 X 0 X^2 X X X 0 X^2 0 1 1 X 1 1 0 1 1 0 1 X^2 1 1 1 X X 1 X^2 X^2 X^2 0 1 X^2 X X 1 0 X 0 X 0 0 X X^2+X 0 0 X X^2+X X^2 0 X^2+X X^2 X^2+X X^2 X X^2+X X X X 0 0 0 X^2+X X^2 0 X X^2 X 0 0 X 0 X X^2 0 X^2+X X X X X^2 X^2 X^2+X X^2+X X^2 X X X X X X^2 X^2 X^2+X X X^2+X X^2+X 0 X X X X^2 X X X^2 0 0 0 0 X X 0 X^2+X X 0 0 X^2+X X 0 X X^2 X X^2 0 X^2+X X 0 X^2+X X^2 X X^2 X^2+X 0 0 X^2+X X X^2 X^2 X^2 X^2+X X X X X^2+X X X^2+X X^2 X^2 X^2+X X^2 X X 0 X^2+X 0 X^2 X^2+X X 0 X^2 X X X^2 0 0 X^2 X^2 0 0 0 X X X^2+X X 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 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 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+48x^56+64x^57+144x^58+136x^59+268x^60+352x^61+406x^62+512x^63+709x^64+1070x^65+1122x^66+1274x^67+1377x^68+1404x^69+1475x^70+1320x^71+1164x^72+884x^73+667x^74+692x^75+375x^76+272x^77+198x^78+136x^79+118x^80+46x^81+64x^82+26x^83+23x^84+4x^85+15x^86+8x^88+3x^90+5x^92+2x^94 The gray image is a linear code over GF(2) with n=276, k=14 and d=112. This code was found by Heurico 1.16 in 22.5 seconds.