The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 X X X 1 X 1 1 1 1 X 1 X X 1 1 1 1 1 1 1 1 1 X 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 2 2 2 0 0 2 2 2 2 0 0 0 0 0 0 2 2 0 2 2 2 2 2 2 0 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 2 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 0 2 0 2 2 2 0 0 2 0 0 2 0 0 2 2 0 0 0 0 0 2 0 0 2 0 2 2 0 0 0 2 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 0 2 2 2 0 2 0 0 2 2 2 0 0 2 0 0 0 0 2 2 0 0 0 2 0 0 2 0 0 0 2 0 0 0 0 2 2 0 2 0 0 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 0 2 2 2 0 2 2 2 0 0 0 0 0 2 0 0 0 2 2 2 2 0 0 0 2 2 2 2 0 2 0 2 0 2 0 0 2 0 2 2 0 0 2 0 2 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 2 0 0 2 0 0 2 2 0 0 0 2 2 0 0 2 0 0 2 0 2 2 2 0 0 2 0 2 2 2 2 0 2 2 0 0 2 0 2 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 2 0 0 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 2 2 2 0 0 2 2 0 0 2 2 0 0 2 0 2 0 0 2 2 0 2 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 0 2 0 0 0 0 0 2 2 0 2 2 2 2 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 0 2 0 0 0 2 2 2 2 0 0 0 2 0 2 0 0 0 2 0 2 2 0 2 2 2 0 2 2 0 2 0 2 2 2 2 2 2 2 0 0 0 2 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 0 2 2 0 0 2 2 2 2 2 2 2 2 0 0 2 2 2 0 2 0 2 0 2 0 0 2 2 0 0 0 2 0 2 2 0 0 2 0 0 0 generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+137x^56+2x^58+209x^60+90x^62+370x^64+228x^66+2048x^67+357x^68+164x^70+239x^72+26x^74+115x^76+2x^78+80x^80+23x^84+4x^88+1x^112 The gray image is a code over GF(2) with n=268, k=12 and d=112. This code was found by Heurico 1.16 in 2.52 seconds.