The generator matrix 1 0 1 1 1 X^2+X 1 1 X^3+X^2 1 1 X^3+X 1 1 0 1 1 X^2+X 1 1 1 X^3+X^2 X^3+X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 X+1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 1 X^3+X X^3+1 1 0 X+1 1 X^2+X X^2+1 1 X^3+X^2 X^3+X^2+X+1 X^2+1 1 1 X^3+1 X^2+X X^3+1 X+1 X^3+X^2+X+1 X^3+1 X+1 X+1 X^3+X+1 X^3+X^2+X+1 X^3+1 X+1 1 0 0 0 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 0 0 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 0 X^3 0 generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 32. Homogenous weight enumerator: w(x)=1x^0+79x^32+84x^33+261x^34+608x^35+566x^36+920x^37+556x^38+608x^39+241x^40+84x^41+77x^42+6x^44+2x^48+1x^50+1x^56+1x^58 The gray image is a linear code over GF(2) with n=296, k=12 and d=128. This code was found by Heurico 1.16 in 0.125 seconds.