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 2 1 2 1 1 1 X 1 1 1 X 1 0 1 0 0 1 2 1 1 2 X 1 2 1 1 X 1 1 1 2 1 1 X 1 1 1 X 1 X 0 X X 0 X 0 0 0 X X+2 X 0 2 2 0 X X+2 X X+2 X+2 X+2 X+2 2 0 0 X+2 2 X+2 0 2 X X 2 X 0 X X+2 X X+2 X X+2 X+2 2 2 X+2 X+2 X X X+2 2 0 2 X X+2 2 0 0 2 0 0 X X 2 X 0 0 2 0 2 X+2 X+2 X+2 0 0 2 2 2 2 2 0 0 0 X 0 X X X+2 0 0 0 X+2 X+2 X X 2 0 X 2 0 X+2 X+2 2 X+2 2 0 2 X 2 X X X 2 X 0 0 0 X+2 X X+2 X X X+2 2 X+2 X X+2 0 2 0 X+2 2 X X X+2 X X 0 X X+2 0 0 X 2 X X 2 X+2 0 X+2 X+2 X X+2 0 0 0 X+2 X 0 0 0 X X 0 X+2 X 2 X+2 X 2 2 X X 2 0 X+2 0 X 2 X X 0 0 X 2 X+2 X+2 X X 2 2 0 X X+2 2 2 2 0 0 X X 2 2 X X 0 X X 0 X 0 X X 0 X X+2 X+2 0 X X X+2 X+2 X+2 X+2 2 X+2 X 0 X+2 2 2 X+2 X X+2 X 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 0 2 2 0 2 0 2 2 2 0 0 2 2 0 0 0 0 2 0 0 0 0 2 2 2 2 2 0 0 2 0 2 2 2 2 0 2 2 2 2 2 2 0 2 2 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 0 2 0 0 2 2 0 2 2 0 0 0 2 2 2 0 0 2 0 2 2 0 2 0 0 2 2 2 2 0 0 0 2 0 0 2 2 2 0 2 2 2 2 2 0 0 0 0 0 0 2 0 0 2 2 2 2 0 2 2 0 0 2 2 0 2 0 2 2 2 0 0 0 0 0 0 0 2 2 2 2 0 0 2 0 0 0 0 0 2 0 2 0 2 2 2 2 2 2 0 0 0 0 2 0 0 2 0 2 2 2 0 2 0 0 2 2 0 0 0 0 2 2 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 2 0 0 2 0 2 2 2 2 2 generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+103x^68+270x^70+32x^71+359x^72+144x^73+401x^74+236x^75+502x^76+240x^77+469x^78+204x^79+332x^80+112x^81+239x^82+36x^83+153x^84+16x^85+109x^86+4x^87+70x^88+44x^90+13x^92+4x^94+2x^96+1x^116 The gray image is a code over GF(2) with n=308, k=12 and d=136. This code was found by Heurico 1.16 in 1.75 seconds.