The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 2 X 2X X 2X+2 1 1 1 1 X X X X 1 1 1 1 2X+2 2X+2 0 2X 1 1 1 1 0 X 2 3X+2 2X X+2 2X+2 3X 0 3X+2 2 3X 2X X+2 2X+2 X 3X+2 X 3X X X+2 X X X 0 2 2X 2X+2 0 2 2X 2X+2 3X+2 3X X+2 X 2 2X+2 2X+2 2X+2 0 2X 3X+2 X+2 generates a code of length 44 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 44. Homogenous weight enumerator: w(x)=1x^0+118x^44+4x^46+4x^50+1x^56 The gray image is a code over GF(2) with n=352, k=7 and d=176. This code was found by Heurico 1.16 in 0.032 seconds.