The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 X X 1 X 1 1 1 1 1 1 1 1 1 1 X^2 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 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 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 0 generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 33. Homogenous weight enumerator: w(x)=1x^0+12x^33+15x^34+79x^36+40x^37+79x^38+15x^40+12x^41+1x^42+1x^44+1x^62 The gray image is a linear code over GF(2) with n=148, k=8 and d=66. This code was found by Heurico 1.16 in 1.01 seconds.