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 X^2 1 1 1 1 1 X 1 1 1 1 1 1 1 1 X X X 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^2 X^3 X^3+X^2 X^3+X^2 0 X^3 X^3+X^2 X^2 0 0 X^3+X^2 X^2 X^3 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^2 X^3 0 0 X^3+X^2 X^3+X^2 X^2 0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^2 0 X^3+X^2 0 X^3+X^2 X^3+X^2 X^3 X^2 0 X^3+X^2 X^2 X^3 0 0 0 0 X^3 X^3 0 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 0 0 X^3 0 0 0 0 0 X^3 0 0 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 0 0 0 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 0 0 0 0 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 0 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 0 0 X^3 0 0 0 X^3 0 0 X^3 0 X^3 generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+10x^69+37x^70+34x^71+89x^72+44x^73+121x^74+62x^75+1147x^76+300x^77+70x^78+14x^79+42x^80+12x^81+3x^82+18x^83+1x^84+18x^85+24x^86+1x^142 The gray image is a linear code over GF(2) with n=608, k=11 and d=276. This code was found by Heurico 1.16 in 5.03 seconds.