The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 1 X+2 1 1 0 1 0 1 1 X+2 1 1 1 0 1 1 2 1 1 X+2 1 1 1 1 1 1 1 X+2 1 1 2 1 1 1 X+2 1 1 1 1 X+2 1 X 1 1 1 0 0 1 1 1 X 1 1 1 1 0 1 X+2 1 1 0 X 2 1 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 0 X+1 1 X+2 3 1 3 1 X+2 X+1 1 0 0 X+1 1 X+2 3 1 1 0 1 X X+3 X+2 2 3 0 X+1 1 0 X+2 1 X+1 X+3 X+3 1 2 X 3 X+2 1 X+2 1 X+2 X X+1 1 1 X+1 X+3 3 0 2 X+2 2 X+2 1 3 1 X+1 X+3 X 1 X 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 2 0 2 2 0 2 0 2 0 2 2 0 0 0 2 2 2 0 0 2 0 0 2 2 0 0 0 0 0 2 2 0 0 2 2 0 0 2 2 0 2 0 2 2 2 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 0 2 0 2 0 2 0 2 2 2 2 2 2 0 2 0 0 2 2 2 2 0 0 2 2 0 0 2 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 2 0 2 0 2 0 0 0 2 0 2 0 2 0 0 2 2 2 0 2 0 0 0 0 0 2 0 0 0 0 2 2 0 2 2 0 0 2 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 2 2 2 2 0 0 2 2 2 0 0 2 0 2 0 2 0 0 0 0 0 0 0 2 2 2 2 0 2 0 2 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 2 2 0 2 0 0 0 0 2 0 2 0 2 2 2 0 2 2 2 0 0 2 2 0 0 0 2 0 2 0 0 2 2 0 2 2 2 2 0 2 0 0 0 0 0 2 2 0 2 0 0 2 2 0 2 0 2 0 0 0 0 0 0 2 0 2 0 0 0 2 0 2 0 2 2 2 2 2 2 2 0 0 0 0 2 2 2 0 2 2 0 2 2 2 0 2 2 2 0 0 0 2 2 0 2 2 2 2 0 2 2 0 0 2 2 0 2 0 0 2 0 2 2 0 0 2 0 0 2 2 0 2 0 2 0 0 0 0 0 0 0 2 2 0 2 0 0 2 2 2 2 0 2 0 2 0 2 2 2 0 2 0 0 2 0 2 2 2 2 0 0 2 0 2 0 2 0 0 2 2 0 0 0 2 0 2 0 2 0 2 2 0 0 2 0 0 2 2 0 2 2 2 2 2 2 2 0 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+34x^68+58x^69+124x^70+224x^71+179x^72+332x^73+216x^74+444x^75+212x^76+468x^77+267x^78+404x^79+233x^80+368x^81+122x^82+196x^83+86x^84+50x^85+22x^86+12x^87+13x^88+4x^89+5x^90+4x^92+3x^94+6x^96+8x^98+1x^106 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 1.32 seconds.