The generator matrix 1 0 0 1 1 1 2X 1 1 1 1 2X+2 2 2 1 1 X+2 1 3X+2 1 1 1 2X 1 1 0 X 3X+2 1 3X+2 1 X X+2 X+2 1 1 2 0 0 1 1 1 0 1 0 2X 2X+3 3 1 X 3X+3 3X X+3 1 X 1 3X+1 0 1 2X+2 X 2X+1 3X+1 2X+3 1 X+2 X 1 1 2 2 1 X+3 1 1 2X 3X+2 2X 1 3X 2 1 3 3X+3 0 0 1 3X+1 X+1 2X 3X+1 3X 1 2X+1 X X 1 3X+3 2X+2 3X+2 X+2 3 1 1 X+1 X+2 2X+3 3X+1 2 2X+2 2X+1 1 2X+2 3X+3 0 3 2 1 3X X 3 1 1 2X 2X+3 2 generates a code of length 42 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 39. Homogenous weight enumerator: w(x)=1x^0+438x^39+738x^40+668x^41+832x^42+504x^43+358x^44+232x^45+152x^46+110x^47+30x^48+28x^49+4x^51+1x^56 The gray image is a code over GF(2) with n=336, k=12 and d=156. This code was found by Heurico 1.16 in 0.109 seconds.