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 2 2 X 1 2 X 0 1 1 0 X X 2 1 X 1 1 1 1 1 X 1 0 2 1 1 1 2 1 1 1 1 X X 1 1 2 1 X 0 0 X 0 0 0 X X+2 X 0 2 2 X X+2 X X 0 0 0 2 X+2 X+2 2 0 X+2 X+2 X 0 X 2 0 X X X+2 X X 0 2 2 X X 0 0 2 0 2 X+2 X+2 2 2 0 X 0 X+2 0 2 X+2 2 2 2 X X 0 X+2 0 X X 2 0 X 2 X+2 2 0 X+2 X 0 0 X 0 0 X 0 X X X+2 0 0 0 X X X 0 2 X+2 X 0 2 2 0 0 X+2 X X+2 2 2 X+2 X X 0 X+2 2 0 0 0 X+2 2 2 X+2 X 0 X 2 X 0 2 X X X+2 X+2 0 2 X+2 X X+2 X+2 0 X 2 0 X X+2 0 2 2 X+2 0 X+2 X 0 X+2 X X 0 X+2 0 X 0 0 0 X X 0 X+2 X 2 X 2 0 X 2 X+2 X 2 2 X X+2 2 X X+2 X+2 0 X 0 2 2 X+2 2 X 2 0 X+2 0 X 0 X 0 X X X+2 X 0 2 0 0 0 0 2 X X+2 2 0 X+2 X+2 X+2 X 2 X 2 X+2 2 2 2 X+2 2 0 0 X 2 0 2 X+2 2 X+2 X 0 0 0 0 2 0 0 0 2 2 2 2 2 0 0 2 2 0 2 2 0 2 0 0 2 0 0 2 2 2 2 0 2 2 0 2 2 2 2 0 0 2 0 2 2 2 2 2 2 0 2 0 2 2 0 2 0 0 2 0 0 0 0 2 2 0 0 2 0 0 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 2 2 0 0 0 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 2 2 0 0 0 2 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 0 2 2 0 0 0 0 0 0 2 0 2 0 0 2 2 2 0 0 2 0 2 2 2 0 0 0 2 0 2 2 0 2 0 2 2 0 2 0 2 0 0 0 0 0 2 0 2 2 0 2 0 0 0 2 2 2 0 0 2 2 2 0 2 2 2 0 2 0 0 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 2 0 0 0 2 2 2 2 2 2 2 0 0 0 2 2 0 2 0 0 2 2 0 2 2 0 2 0 0 0 0 2 0 2 2 2 2 2 2 2 2 2 2 0 2 0 2 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+188x^68+4x^69+372x^70+60x^71+579x^72+164x^73+656x^74+332x^75+919x^76+460x^77+902x^78+452x^79+891x^80+364x^81+638x^82+164x^83+395x^84+32x^85+254x^86+16x^87+159x^88+106x^90+61x^92+16x^94+2x^96+4x^100+1x^116 The gray image is a code over GF(2) with n=312, k=13 and d=136. This code was found by Heurico 1.16 in 20 seconds.