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 X 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 1 X 1 X 1 1 1 1 1 X X 1 2 1 X 1 2 1 1 1 X 0 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 2 2 2 2 0 2 2 0 2 2 0 2 0 0 2 0 0 2 2 0 0 2 0 0 2 2 2 0 2 0 2 2 2 0 0 2 0 0 2 2 2 0 2 0 2 2 2 0 0 2 0 2 0 0 0 2 0 2 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 2 0 0 0 0 0 2 2 0 0 0 2 0 2 2 2 2 2 0 0 2 0 2 2 0 0 2 0 2 0 0 2 0 0 2 2 0 2 0 2 0 0 2 0 2 2 2 0 2 0 2 0 0 0 0 2 0 0 0 0 0 0 2 2 2 0 2 2 0 2 2 0 0 0 0 0 0 0 0 2 0 2 2 0 2 0 2 2 2 2 2 0 2 0 2 0 0 2 2 2 2 2 2 0 2 2 2 2 2 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 2 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 0 2 0 2 0 2 2 2 0 0 2 0 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 2 0 0 0 2 0 2 2 0 0 2 0 0 2 2 2 2 2 0 2 2 2 2 2 0 2 0 0 2 2 0 2 0 0 2 0 2 2 0 0 0 0 0 2 0 0 0 2 0 0 2 0 0 2 2 2 2 0 2 0 2 2 0 2 0 0 2 2 2 0 2 2 2 0 0 0 0 0 2 2 2 0 0 2 2 2 2 0 0 0 0 2 0 2 0 0 2 2 2 2 0 2 0 0 2 2 0 2 2 0 2 0 2 0 0 2 0 0 0 0 0 0 2 0 0 2 0 2 0 2 0 0 0 2 0 0 0 2 2 2 2 2 0 0 2 0 2 0 0 0 2 2 2 2 0 2 2 2 0 0 0 2 2 0 0 2 0 2 2 0 0 0 2 2 0 0 0 0 2 0 2 2 2 2 2 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 2 0 0 2 2 2 0 0 2 2 2 2 0 0 2 0 0 0 0 2 2 0 0 2 0 2 2 2 0 0 0 2 0 0 2 2 2 0 0 2 0 2 0 0 0 2 2 0 0 0 0 2 0 0 2 2 0 0 2 0 2 2 0 0 0 0 0 0 0 0 0 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 2 0 2 0 2 2 2 0 2 2 2 0 2 0 2 2 2 2 2 2 2 0 2 2 0 2 0 0 0 0 2 2 0 0 0 2 0 2 2 0 2 2 0 2 0 0 0 0 0 0 2 0 0 2 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+72x^68+6x^70+152x^72+72x^74+455x^76+612x^78+419x^80+72x^82+81x^84+6x^86+58x^88+26x^92+10x^96+4x^100+1x^108+1x^132 The gray image is a code over GF(2) with n=312, k=11 and d=136. This code was found by Heurico 1.16 in 0.794 seconds.