The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 X+2 1 1 1 0 1 0 1 1 X+2 1 1 0 X+2 1 1 1 0 1 1 1 X+2 1 1 1 1 1 1 1 1 0 X+2 1 1 1 0 1 0 1 1 1 1 X+2 1 1 1 X+2 1 1 1 X 1 1 1 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 X+2 1 X+1 0 3 1 2 1 X+1 X+2 1 3 0 1 1 X+1 3 X+2 1 X+1 0 3 1 X+2 0 X+2 3 X+1 X+3 X+2 0 1 1 X+2 3 X+1 1 0 1 X X+1 X 3 1 3 X 2 1 X+1 X+2 0 X X+1 X+1 X+1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 2 0 0 2 2 2 2 2 2 0 2 2 2 0 0 0 2 2 0 2 0 0 2 0 2 2 2 0 2 2 2 0 0 2 0 2 0 2 2 0 0 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 2 0 2 2 2 2 2 0 2 0 0 2 2 0 2 2 2 2 2 2 0 0 0 0 0 2 2 0 2 0 0 0 2 0 0 0 2 0 0 2 2 2 0 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 2 2 0 0 2 0 2 0 2 2 0 2 0 2 0 0 2 0 2 0 0 2 2 0 0 2 2 2 0 0 2 2 0 0 2 2 0 2 0 2 0 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 2 2 2 2 2 0 2 2 2 0 0 0 0 2 2 0 2 0 0 0 0 0 0 2 2 2 0 0 0 2 0 2 0 2 0 2 2 2 0 0 2 0 2 0 2 2 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 2 0 2 2 0 2 0 2 0 2 0 0 0 2 0 0 2 0 2 0 2 2 0 2 2 2 2 2 2 0 2 0 0 0 2 0 2 0 0 0 0 2 0 2 2 0 2 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 2 2 2 0 0 0 2 0 2 0 0 2 2 2 0 2 0 2 2 0 2 0 0 2 0 0 0 0 2 0 2 2 2 2 0 0 0 2 2 0 2 2 2 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 2 2 0 2 2 2 0 2 2 0 0 0 2 2 2 0 2 0 0 0 2 2 0 0 0 2 0 2 2 0 2 2 2 0 2 0 2 2 0 0 0 0 0 2 2 2 0 2 2 2 0 2 0 0 0 0 0 0 0 0 0 2 2 0 2 0 2 2 0 2 2 2 2 2 0 2 2 0 2 0 0 2 2 2 2 0 2 2 0 0 2 2 2 2 0 0 2 2 0 0 0 2 0 2 2 2 0 2 2 0 0 0 2 0 0 2 2 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+173x^56+166x^58+794x^60+1324x^62+2484x^64+3252x^66+3384x^68+2336x^70+1468x^72+566x^74+284x^76+36x^78+78x^80+32x^84+3x^88+2x^92+1x^96 The gray image is a code over GF(2) with n=268, k=14 and d=112. This code was found by Heurico 1.16 in 16.6 seconds.