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 X X 0 X 1 X 1 1 X X^2 X 1 0 1 X 1 1 1 1 X^2 X^2 1 1 X^2 1 1 0 X 1 X^2 1 1 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X X^2 X^2 X^2+X 0 X X^2+X 0 X X^2 X X X^2 X^2+X 0 0 X^2 X^2+X X^2+X X^2 X^2+X X X X X^2 X X 0 X^2 X X^2+X 0 X X X X^2+X X 0 X^2 X X^2+X X^2 X X^2+X 0 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X X X^2 0 X^2+X X^2+X X X^2 0 X^2 X X 0 X^2+X X X X^2+X 0 X^2 0 X X^2+X X^2+X X^2 0 X^2+X X X^2+X X 0 X^2+X X^2+X X^2+X X 0 X^2+X X^2 X 0 X X 0 X^2+X 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 50. Homogenous weight enumerator: w(x)=1x^0+33x^50+72x^51+126x^52+132x^53+213x^54+244x^55+314x^56+398x^57+367x^58+422x^59+395x^60+346x^61+281x^62+230x^63+128x^64+118x^65+88x^66+42x^67+52x^68+26x^69+32x^70+14x^71+4x^72+4x^73+7x^74+3x^76+1x^78+1x^80+1x^82+1x^86 The gray image is a linear code over GF(2) with n=236, k=12 and d=100. This code was found by Heurico 1.16 in 1.19 seconds.