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 2 X X 2 1 X X 1 1 1 1 0 1 X 1 X 1 1 X X 1 0 X 2 1 X 1 2 2 1 1 2 1 X X X 0 1 0 1 X 1 0 X 0 0 0 X X+2 X 0 2 2 X X+2 X X 0 0 0 2 X+2 X+2 2 X+2 X X+2 0 0 X+2 0 X X 2 X 2 X+2 0 X X X X X 2 X X X 2 0 0 2 X 2 2 X+2 2 X 0 X 0 2 2 0 0 X+2 X 0 X 0 2 0 0 X+2 2 0 X X X X+2 2 0 0 0 X 0 X X X+2 0 0 0 X X X 0 2 X+2 X 0 2 2 0 0 X+2 2 X X+2 2 X+2 X+2 0 X X+2 X X 0 2 2 X X+2 2 2 0 X X+2 2 0 2 2 X 0 X+2 X+2 X 2 2 X 0 2 X X 2 2 2 X 2 X 0 X+2 X X 2 X X 2 0 X X+2 X 2 0 0 0 X X 0 X+2 X 2 X 2 0 X 2 X+2 X 2 2 X X+2 2 X 0 X X+2 X+2 0 X+2 0 0 0 X+2 X+2 2 2 2 2 0 2 X+2 X 2 2 2 X X+2 X 0 2 X+2 X+2 2 X 2 2 X+2 0 0 X 0 X 0 X+2 2 X 0 X+2 X+2 2 2 2 X+2 0 0 X+2 X+2 X+2 0 X+2 0 0 0 0 2 0 0 0 2 2 2 2 2 0 0 2 2 0 2 2 0 2 2 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 0 0 0 2 0 0 2 2 2 0 2 2 0 2 2 0 0 0 2 0 0 2 0 0 2 0 2 2 2 2 2 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 2 2 0 0 0 2 0 0 0 0 2 2 0 0 2 2 2 0 2 0 0 2 2 2 2 0 0 0 0 0 2 2 2 0 0 2 0 2 0 0 0 2 2 0 0 2 0 0 2 0 0 0 2 0 2 2 2 0 2 2 2 0 0 0 0 0 0 2 0 2 0 0 2 2 2 0 0 2 0 2 2 2 0 2 0 0 0 2 0 0 0 2 2 0 2 0 2 2 2 2 0 0 2 0 2 0 0 2 0 0 0 0 2 2 0 0 0 2 0 2 2 2 0 2 0 2 2 0 0 2 0 2 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 0 2 0 2 0 2 2 0 0 2 2 2 0 0 0 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 2 0 0 0 0 2 0 2 0 2 0 0 2 2 2 2 2 2 0 2 2 2 0 generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+57x^68+90x^69+144x^70+220x^71+309x^72+358x^73+390x^74+450x^75+484x^76+616x^77+748x^78+710x^79+642x^80+590x^81+465x^82+446x^83+389x^84+300x^85+210x^86+162x^87+118x^88+68x^89+68x^90+56x^91+38x^92+26x^93+17x^94+4x^95+9x^96+5x^98+1x^104+1x^110 The gray image is a code over GF(2) with n=316, k=13 and d=136. This code was found by Heurico 1.16 in 7.8 seconds.