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 1 X+2 1 1 0 1 1 X+2 1 1 1 1 1 X 1 1 1 X 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X+2 1 1 1 X 1 1 1 1 X+2 1 X+2 1 0 1 1 1 0 0 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 0 X+2 X+1 1 X+2 X+1 1 0 2 1 3 X+2 X+2 X+1 X 1 0 1 X+3 1 2 1 3 0 X+1 1 0 2 X+2 2 X+2 X+3 X X X+1 X+1 1 0 2 X 1 X+3 3 3 1 1 X+3 1 X+3 1 X+1 X+2 0 1 1 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 0 2 0 2 2 0 2 2 2 0 2 0 2 2 0 2 2 0 2 0 2 0 0 0 0 2 2 2 0 0 0 0 2 2 0 2 2 0 0 2 2 2 0 2 2 2 0 2 2 2 2 2 2 2 0 2 0 0 0 2 0 0 0 0 0 2 0 2 2 0 2 0 2 0 2 0 2 2 0 0 2 0 0 2 0 0 0 2 0 2 0 2 2 2 0 2 2 0 2 2 0 0 2 2 0 2 0 0 2 0 2 2 0 0 0 2 0 0 0 0 0 2 2 2 2 0 2 0 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 2 2 0 0 2 0 0 2 0 2 0 0 0 0 0 2 2 0 0 2 2 2 0 2 2 0 0 2 0 2 0 2 0 2 0 2 0 2 2 2 2 0 0 2 0 2 2 2 2 0 0 2 0 0 0 0 0 0 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 0 2 2 0 2 2 0 0 0 2 0 2 0 0 2 2 2 0 2 0 2 2 0 2 0 0 2 0 2 0 2 2 0 2 2 2 2 0 2 0 2 0 2 2 0 0 2 2 0 2 0 0 0 0 2 2 0 0 0 0 0 0 2 0 2 0 0 0 2 0 2 0 2 2 2 2 2 0 0 0 2 2 2 0 2 2 2 2 0 2 0 0 2 0 0 0 0 0 0 2 2 0 0 2 0 2 2 0 2 2 0 0 2 2 0 2 0 0 2 2 2 2 2 0 2 2 2 2 2 0 2 2 0 0 0 0 0 0 0 2 2 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 2 0 2 0 0 0 2 0 2 0 0 2 0 2 0 2 0 2 0 2 0 0 0 2 2 2 2 2 2 2 0 2 0 2 0 0 2 0 2 0 0 2 2 2 2 2 2 0 2 2 2 2 generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+124x^68+68x^69+196x^70+204x^71+313x^72+324x^73+252x^74+428x^75+318x^76+428x^77+252x^78+324x^79+280x^80+204x^81+196x^82+68x^83+83x^84+15x^88+8x^92+6x^96+3x^100+1x^112 The gray image is a code over GF(2) with n=304, k=12 and d=136. This code was found by Heurico 1.16 in 1.98 seconds.