The generator matrix 1 0 0 1 1 1 X 1 1 X+2 1 1 X 2 0 0 1 1 X+2 1 X+2 1 1 1 2 1 1 X 1 1 1 0 X X 1 1 1 X X 1 0 1 1 X+2 X+2 2 2 1 0 2 1 X 1 1 0 X+2 1 2 1 1 1 1 2 1 1 1 0 0 0 1 2 1 2 1 1 2 1 2 0 1 0 X 1 X+3 1 X+2 0 2 1 X+1 X+2 1 1 1 X+2 3 1 X+3 1 2 3 X X+2 X+2 X+1 1 X+3 2 2 1 X 1 3 X+1 X+1 1 1 0 0 X+1 X 1 1 1 X+2 0 1 1 3 1 1 X+1 0 0 1 1 X+3 1 2 3 1 X X+2 2 0 1 X X+2 0 X 0 X+1 2 1 1 1 0 0 1 1 X+3 X+2 1 X+1 X+2 1 3 0 1 X X+1 3 2 X+2 0 1 X+1 1 0 X 1 1 X+1 X 2 3 2 1 1 0 X+2 1 X+2 1 0 X+1 1 X+1 0 X+1 X X+3 1 X+1 3 0 X+3 2 X 2 1 1 0 X+3 1 X+1 3 X+1 1 X+2 X+3 X+3 1 X+2 1 0 1 X+1 1 X+1 2 X+1 X+1 X 0 0 0 2 0 0 0 0 2 2 0 0 0 2 0 2 0 0 0 2 2 2 2 0 0 0 2 2 2 2 0 2 2 0 2 2 2 2 0 2 0 0 0 2 0 0 0 2 0 2 0 2 0 2 2 2 0 0 0 0 0 2 0 2 2 0 2 0 0 2 2 2 2 0 2 0 2 0 0 0 0 0 2 0 0 2 2 2 0 2 2 0 2 2 0 0 0 0 0 0 2 2 0 0 0 2 0 2 2 2 0 2 0 2 2 0 0 0 2 0 0 2 2 2 0 2 0 0 2 0 0 2 0 2 2 0 2 0 2 0 0 2 2 0 2 2 2 2 2 0 2 2 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 0 2 2 2 2 0 0 2 0 2 2 2 0 0 2 0 2 0 2 0 2 2 0 2 0 0 2 0 2 2 0 2 0 2 2 2 2 2 2 2 2 0 0 2 2 2 2 0 0 0 0 2 2 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 2 2 0 2 2 0 0 2 2 0 0 2 0 0 2 0 2 0 2 2 0 2 0 0 2 2 2 0 2 2 0 0 2 0 0 0 0 0 0 2 0 2 2 0 2 2 0 0 2 2 2 2 0 2 2 0 2 0 2 0 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+136x^70+228x^71+485x^72+422x^73+638x^74+664x^75+772x^76+600x^77+722x^78+530x^79+734x^80+488x^81+473x^82+342x^83+352x^84+180x^85+193x^86+78x^87+77x^88+34x^89+8x^90+10x^91+4x^92+4x^93+4x^94+4x^95+7x^96+1x^98+1x^102 The gray image is a code over GF(2) with n=312, k=13 and d=140. This code was found by Heurico 1.16 in 4.62 seconds.