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 X 0 X 0 1 1 X 0 1 1 0 1 1 1 1 X 1 1 X 1 0 1 1 0 1 X 1 1 X 1 X 1 1 1 1 1 1 X 1 1 2 1 X 0 X 0 X+2 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 0 2 X+2 X 0 0 X+2 X 2 X+2 X+2 X X+2 X X+2 0 X+2 X 2 X X X+2 0 X+2 2 X+2 2 2 X+2 X+2 X X+2 0 X X X+2 X+2 2 X+2 0 X+2 2 X X+2 X X+2 0 X X X 2 0 X+2 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 2 0 0 0 2 2 2 2 2 0 0 2 0 0 2 2 2 2 2 0 0 0 0 0 2 0 0 0 2 2 0 0 2 0 2 2 2 0 0 2 0 0 2 2 2 2 0 2 2 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 0 0 0 2 2 0 2 2 0 2 2 2 2 2 2 2 2 2 2 0 2 0 2 2 0 2 0 2 2 2 0 2 0 0 2 0 0 2 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 2 2 2 2 0 2 0 2 0 0 2 2 2 0 0 2 2 0 2 2 2 2 2 0 0 0 0 0 2 0 0 2 2 0 0 2 0 0 0 2 0 2 0 2 2 0 0 0 2 2 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 2 2 0 0 2 2 0 0 2 0 2 2 0 2 2 0 2 2 0 0 0 2 0 0 2 0 2 2 0 0 0 0 2 0 0 2 2 2 2 0 0 2 2 0 0 2 0 0 2 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 2 0 2 2 2 2 0 2 0 2 0 0 0 2 0 2 2 2 0 0 2 2 0 0 0 2 2 0 2 2 2 2 2 2 2 0 2 2 0 2 2 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 2 2 2 0 2 2 0 0 2 2 2 2 0 2 2 2 2 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 0 2 0 0 2 2 2 0 0 0 2 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 0 0 2 0 2 2 2 2 0 2 2 2 2 2 0 2 0 0 0 2 2 2 0 0 2 2 0 2 2 2 2 0 2 2 0 2 2 2 2 0 2 2 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 2 2 0 2 0 0 2 2 2 0 2 2 0 0 0 2 0 2 2 2 0 0 2 0 0 0 2 2 2 2 2 2 2 0 2 0 0 2 0 0 0 2 2 2 0 2 2 0 0 2 2 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+160x^56+132x^58+495x^60+594x^62+1225x^64+1464x^66+1635x^68+1060x^70+776x^72+308x^74+211x^76+26x^78+71x^80+26x^84+6x^88+1x^96+1x^100 The gray image is a code over GF(2) with n=268, k=13 and d=112. This code was found by Heurico 1.16 in 6.8 seconds.