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 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 2 1 1 X 1 0 1 X 1 0 1 X 1 X 1 0 X 1 1 2 1 2 1 1 X 0 X 0 X 0 0 X X+2 0 2 X X+2 0 X X 2 2 X+2 X+2 2 0 X+2 0 X+2 X+2 X 0 2 0 X+2 X 0 2 X X 0 0 X X+2 2 X+2 2 X 2 0 X+2 X+2 0 0 2 2 X+2 X 2 X 2 X X 0 0 X+2 0 X X X+2 2 2 0 X+2 0 2 X 2 2 2 2 X+2 0 0 X X 0 X+2 X 0 2 X X 0 0 X+2 2 X+2 2 0 X+2 X 2 X X 0 0 X X+2 0 2 2 X X+2 X+2 2 0 2 2 X+2 X X X+2 X+2 0 2 X 2 X+2 0 0 0 X 2 X+2 2 0 X X+2 2 2 X+2 0 X 0 X+2 0 X 2 X 0 0 2 X+2 0 2 X+2 X+2 2 0 0 0 2 0 0 0 2 2 2 0 0 2 2 2 2 0 0 2 2 0 2 0 2 0 0 0 0 0 2 0 2 0 0 2 2 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 0 2 2 2 0 2 0 2 0 2 2 0 2 2 0 2 2 2 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 2 2 0 2 0 0 2 0 0 0 2 0 2 0 2 2 2 2 0 0 2 0 0 2 2 0 2 2 0 2 2 0 2 2 2 2 0 0 2 2 0 0 0 2 0 0 0 2 0 2 0 2 2 2 2 2 2 2 2 0 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 2 2 0 2 0 2 0 2 2 2 2 0 0 2 0 0 2 0 2 2 0 2 2 0 2 0 0 2 0 2 0 0 0 2 0 0 2 2 0 2 2 2 2 0 2 0 2 2 2 0 2 2 0 0 2 2 0 0 0 0 0 0 2 2 0 2 2 0 0 0 0 0 0 0 2 2 2 2 0 2 2 2 0 2 0 2 2 0 2 0 2 0 2 0 0 2 0 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 2 2 0 2 0 2 0 2 0 0 2 0 2 2 0 0 2 2 2 2 2 0 0 2 2 2 2 2 0 2 2 2 generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+180x^70+8x^71+93x^72+140x^73+199x^74+168x^75+54x^76+396x^77+164x^78+184x^79+72x^80+100x^81+118x^82+24x^83+16x^84+4x^85+76x^86+17x^88+27x^90+2x^92+4x^94+1x^128 The gray image is a code over GF(2) with n=308, k=11 and d=140. This code was found by Heurico 1.16 in 36.6 seconds.