The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 X 1 X 1 1 1 0 1 0 1 X 1 1 1 1 1 X 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X X^2+X X 0 X^2+X X^2 X^2+X X^2+X X X^2+X X X^2+X X 0 X^2+X 0 X^2+X X X^2+X 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 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 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 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 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 0 generates a code of length 33 over Z2[X]/(X^3) who´s minimum homogenous weight is 24. Homogenous weight enumerator: w(x)=1x^0+52x^24+10x^25+50x^26+54x^27+126x^28+196x^29+276x^30+460x^31+539x^32+616x^33+521x^34+456x^35+252x^36+188x^37+117x^38+52x^39+48x^40+14x^41+52x^42+2x^43+6x^44+6x^46+1x^50+1x^54 The gray image is a linear code over GF(2) with n=132, k=12 and d=48. This code was found by Heurico 1.16 in 0.491 seconds.