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 X 2 X 1 X 0 0 1 X 1 0 1 2 1 X 1 0 1 1 X 1 1 1 X 1 X 0 0 1 1 X X 2 2 1 1 1 X 0 1 1 2 1 1 0 X 0 X 0 0 X X+2 0 2 X 0 X+2 2 X+2 X X+2 0 X 0 X 2 0 X X 0 X+2 X X 0 2 0 2 0 2 X X X 2 2 0 X 2 X+2 0 2 0 X X+2 X+2 X X X+2 X+2 2 0 0 X+2 2 0 0 2 X X X X 2 0 0 X X+2 0 X X 0 X+2 2 X+2 X+2 0 0 X X 0 X+2 X 0 0 X X 2 2 X+2 X 2 0 0 X 0 X X X+2 0 X+2 X+2 X 2 X+2 0 0 X+2 X+2 0 2 X X+2 X+2 X X X 2 0 0 X X 2 X 2 2 X+2 0 0 0 X 0 2 2 X+2 X X+2 X X 2 X+2 X X+2 X X 2 2 X+2 X X+2 2 X X X X+2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 0 0 2 2 2 0 2 2 2 0 0 2 0 2 2 0 2 2 2 2 2 2 2 2 2 0 2 0 0 2 2 0 2 0 2 2 0 2 0 0 2 0 2 2 0 2 2 2 0 2 2 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 0 0 0 0 2 2 2 0 0 2 2 0 2 2 2 0 0 2 2 0 2 2 2 2 2 2 2 0 2 2 0 0 2 0 0 0 2 2 2 2 0 0 0 2 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 2 0 2 2 0 0 2 2 2 0 2 0 2 0 0 2 2 2 0 2 2 0 0 2 2 0 0 2 2 0 2 2 2 2 2 0 0 2 0 0 0 2 2 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 2 0 2 2 2 2 2 0 2 2 2 2 2 2 0 2 0 0 0 0 2 2 2 0 2 0 2 0 0 2 0 2 0 0 0 0 2 2 2 0 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 2 0 0 2 2 0 2 0 2 2 2 2 0 0 2 2 2 2 2 2 2 0 0 0 0 0 2 2 0 0 0 0 2 0 0 2 2 0 2 0 2 0 2 2 2 0 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 0 2 2 2 2 2 0 0 2 2 0 2 2 0 0 0 0 2 0 2 2 0 2 2 0 2 0 2 0 0 2 0 2 2 0 2 0 2 0 0 0 0 0 2 2 2 0 0 2 0 0 0 0 2 2 0 2 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+126x^68+226x^70+40x^71+487x^72+124x^73+560x^74+232x^75+869x^76+392x^77+894x^78+472x^79+958x^80+384x^81+688x^82+248x^83+531x^84+120x^85+334x^86+32x^87+237x^88+4x^89+96x^90+83x^92+18x^94+28x^96+7x^100+1x^112 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 7.82 seconds.