The generator matrix 1 0 0 0 1 1 1 1 X 1 1 X 1 X 0 0 0 0 1 1 1 0 X 0 1 X 0 X 1 1 X 1 0 0 1 X 0 0 1 0 0 0 1 X 0 0 1 1 1 X+1 1 X 1 0 1 X X+1 X+1 1 0 1 X 1 1 X 0 1 0 X 1 0 X+1 1 1 0 0 1 0 1 1 1 X 1 X 0 0 1 0 X 1 1 0 1 X+1 X 1 1 X 1 X+1 X+1 1 X X+1 1 1 X+1 1 1 X+1 X+1 0 0 0 1 1 0 0 1 1 X+1 X X+1 1 X+1 1 0 X+1 X 1 X+1 X X+1 1 1 X X 1 0 X+1 1 0 1 X+1 0 1 0 1 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X 0 X 0 X X X 0 X 0 0 X X 0 X 0 0 X X 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X 0 X X X 0 X X X X 0 0 generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 32. Homogenous weight enumerator: w(x)=1x^0+266x^32+382x^36+246x^40+104x^44+23x^48+2x^52 The gray image is a linear code over GF(2) with n=74, k=10 and d=32. As d=32 is an upper bound for linear (74,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10. This code was found by Heurico 1.16 in 11.6 seconds.