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 0 1 0 0 2 1 1 X 1 1 X+2 1 2 1 0 2 2 1 1 1 1 1 X+2 1 0 1 1 1 1 0 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 2 X+3 2 1 X+2 1 1 1 X X 1 X+2 1 1 3 1 3 1 1 1 3 3 X+1 X X+3 1 0 0 2 X X+3 0 X 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 0 2 0 2 2 0 0 2 0 0 0 2 2 2 0 0 2 0 2 0 0 2 2 2 2 2 2 0 0 2 2 0 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 0 2 0 2 0 2 2 0 2 0 2 0 0 2 0 0 2 2 0 2 2 0 2 2 2 0 2 2 0 0 0 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 0 0 2 0 0 2 0 2 0 2 0 2 2 0 0 0 0 2 2 2 2 2 0 0 2 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 0 2 2 2 0 2 0 2 0 0 2 0 0 2 2 0 2 2 0 0 0 0 0 2 0 0 2 2 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 2 2 0 0 0 2 2 0 0 0 2 0 2 2 0 2 0 2 2 0 2 0 0 0 2 0 0 2 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 2 2 2 0 0 0 0 2 2 2 2 0 0 2 0 2 0 2 2 2 0 2 0 0 2 2 2 2 2 2 2 0 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+132x^70+108x^71+184x^72+240x^73+335x^74+312x^75+200x^76+352x^77+367x^78+352x^79+242x^80+368x^81+330x^82+232x^83+104x^84+64x^85+91x^86+20x^87+26x^88+20x^90+1x^94+9x^96+2x^98+1x^102+2x^104+1x^106 The gray image is a code over GF(2) with n=312, k=12 and d=140. This code was found by Heurico 1.16 in 48.6 seconds.