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 1 1 1 1 1 1 1 1 0 2 X 2 0 2 X X X X 2 1 1 1 X X 2 1 X 1 X X 1 2 1 2 1 X 1 1 0 1 X 1 0 X 0 0 0 0 0 0 0 0 2 X X X+2 0 X+2 X+2 0 2 X X+2 2 X X X 2 X 0 X 2 X+2 X X+2 X+2 X+2 X+2 X 2 0 X+2 X+2 2 X X+2 X 0 2 X X+2 0 X 0 2 X X 2 X X+2 0 X X X 0 0 X+2 X+2 X+2 X+2 2 2 X 2 X X 0 X 2 2 2 X 0 0 X 0 0 0 0 0 0 0 X+2 2 X X X X 0 X X 0 X+2 2 0 X+2 X X X+2 X+2 2 0 X+2 0 2 X+2 X 0 2 2 X 0 2 X X+2 X+2 X X 0 2 2 2 X+2 X X X+2 0 X+2 0 X+2 0 0 2 0 X X+2 2 0 0 0 2 X X+2 X 2 X+2 2 X+2 X X 0 0 0 0 0 X 0 0 0 X X+2 X X X+2 0 X 2 0 X+2 X+2 2 X+2 X+2 X 0 2 0 2 X X X 2 X 0 X+2 0 X X+2 0 2 X X 2 X+2 0 2 X 0 0 0 0 2 X 0 X 0 0 2 X+2 2 X+2 2 X+2 X X X+2 0 2 2 0 X+2 X+2 0 2 0 X+2 X+2 X+2 X+2 0 2 X 0 0 0 0 X 0 X X X 2 X X X 2 2 X+2 X+2 2 X+2 2 X+2 X X+2 2 2 X 0 X+2 2 X+2 X+2 X X+2 X 0 X+2 X+2 0 0 2 X 2 0 X+2 2 2 X X X X X X 2 X+2 0 X 0 0 2 2 X+2 X+2 0 X+2 X+2 X X 2 X 0 0 2 0 X X+2 X X+2 X 0 0 0 0 0 0 0 X X 2 X+2 X+2 X X X+2 0 X 2 2 2 X X+2 0 2 2 0 X 0 X 2 2 X+2 X+2 X+2 X+2 0 2 2 2 2 0 0 X+2 X+2 X+2 X+2 X X 2 2 X+2 X+2 X+2 0 X 2 2 2 2 2 X X+2 X X+2 X+2 X X 2 X+2 2 X+2 0 0 2 X X X X+2 2 0 X+2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 0 2 2 0 2 2 0 0 0 0 2 2 2 2 2 2 0 2 0 0 0 2 0 2 2 0 2 2 2 0 2 2 0 0 2 0 0 0 2 2 2 2 0 2 2 0 2 2 0 2 0 2 2 0 0 0 0 generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+155x^68+444x^70+32x^71+681x^72+92x^73+1006x^74+320x^75+1388x^76+688x^77+1598x^78+936x^79+1789x^80+912x^81+1757x^82+656x^83+1313x^84+320x^85+895x^86+104x^87+600x^88+36x^89+351x^90+169x^92+83x^94+45x^96+10x^98+2x^100+1x^116 The gray image is a code over GF(2) with n=320, k=14 and d=136. This code was found by Heurico 1.16 in 28 seconds.