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 X 0 X 1 1 X 1 1 1 1 1 1 0 0 1 X 1 1 X 0 1 X 1 1 0 1 1 1 0 X 1 0 1 X X 1 1 X X 1 0 X X 1 1 X 0 X 0 X+2 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 X 0 2 2 X+2 X+2 0 X+2 0 X 2 0 2 2 X+2 X X X X+2 X X+2 0 0 X+2 X+2 X+2 X X 0 0 X X 0 X+2 X+2 2 X X X+2 X+2 X X X 2 X+2 X X X+2 2 X X X+2 X+2 X+2 0 X 0 2 X X+2 X+2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 0 0 0 2 2 2 2 0 0 0 2 0 2 0 0 0 2 0 0 2 2 2 2 2 0 0 0 2 2 0 2 2 2 0 2 2 2 0 0 0 0 2 0 0 2 2 0 2 0 2 2 0 2 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 2 0 2 0 0 0 0 0 0 2 2 0 0 0 0 0 2 2 0 2 2 2 2 2 2 0 0 2 0 2 2 0 2 2 0 2 2 0 0 2 0 2 0 2 2 2 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 0 0 2 0 2 0 2 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 2 2 0 0 0 0 0 2 2 0 2 2 0 2 2 0 2 0 0 0 2 0 0 2 0 0 2 2 0 2 2 2 0 0 2 2 0 0 0 0 0 0 2 0 0 0 2 0 2 0 0 2 0 0 0 0 2 2 0 2 2 2 2 2 2 0 2 0 2 2 0 0 0 2 2 2 0 2 2 0 0 0 0 2 2 2 2 2 0 0 0 0 2 0 0 0 2 2 0 0 2 0 2 2 2 2 0 2 0 0 2 2 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 0 2 2 2 0 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 0 2 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 2 0 2 0 2 0 0 2 2 0 2 0 2 2 2 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 0 2 2 2 0 0 2 2 2 0 2 2 0 0 0 2 0 2 2 2 0 0 0 2 0 0 2 0 0 0 0 2 2 2 0 2 2 0 0 2 0 2 0 2 2 0 2 2 2 2 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 0 0 2 2 0 2 0 2 2 0 0 0 2 2 2 2 2 0 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 2 2 0 2 0 0 2 2 2 2 0 0 2 2 0 2 2 0 0 2 0 0 0 2 0 0 2 0 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+126x^68+114x^70+352x^72+464x^74+733x^76+612x^78+684x^80+464x^82+286x^84+122x^86+71x^88+16x^90+30x^92+10x^96+8x^100+1x^104+1x^108+1x^112 The gray image is a code over GF(2) with n=312, k=12 and d=136. This code was found by Heurico 1.16 in 2.27 seconds.