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 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 X^2 X 1 1 1 X 0 X^3+X^2 0 X^2 0 0 X^2 X^2 X^3 X^3 X^2 X^3+X^2 0 X^3 X^2 X^2 0 X^3 X^2 X^3+X^2 0 X^3+X^2 X^3 X^3+X^2 0 X^3 X^2 X^3+X^2 0 0 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 0 X^3 X^3 X^3+X^2 X^3 X^2 X^2 0 X^3+X^2 0 X^3 X^3 X^3 X^2 X^3 0 X^3+X^2 X^2 0 0 X^2 0 0 X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^2 X^2 X^3 0 X^3 0 X^3+X^2 0 0 0 X^3+X^2 X^2 0 X^3+X^2 X^3+X^2 0 X^3 X^2 X^2 0 0 X^2 X^3+X^2 0 X^3 X^2 X^2 0 X^2 X^2 X^3 X^3 X^3 X^2 X^3 X^3+X^2 X^2 0 0 X^3+X^2 X^2 0 X^2 X^3 0 X^3+X^2 X^3+X^2 0 X^3 X^3 X^2 0 X^2 X^3+X^2 0 X^3+X^2 X^2 0 X^3 X^3 0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 0 0 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 0 X^2 X^3 X^2 X^3+X^2 0 X^3 X^2 X^3 0 0 0 X^3 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 0 X^3 0 0 0 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 0 0 0 X^3 0 0 X^3 0 X^3 X^3 X^3 generates a code of length 78 over Z2[X]/(X^4) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+57x^72+97x^74+213x^76+256x^77+847x^78+256x^79+192x^80+49x^82+38x^84+29x^86+10x^88+2x^90+1x^148 The gray image is a linear code over GF(2) with n=624, k=11 and d=288. This code was found by Heurico 1.16 in 0.625 seconds.