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 X 1 0 1 1 1 1 X 1 X 1 1 1 0 1 1 1 X 1 1 2 1 0 1 X 1 1 1 1 0 1 1 2 X 2 1 2 0 X 2 1 0 0 X 1 2 0 X X 1 0 0 X 0 0 0 0 0 0 2 X X+2 X+2 X X X+2 X+2 2 2 0 X X X+2 X 0 X X 0 X+2 X 2 2 2 X+2 X+2 0 X+2 X+2 2 X X+2 X+2 X+2 0 X 2 X+2 0 0 X+2 2 2 X X+2 0 X+2 2 0 X+2 X X+2 2 2 2 X 2 0 X X 2 2 2 X+2 X X X X 2 0 X X+2 X+2 X X X+2 X X X 0 0 X 0 0 0 X X+2 X+2 X X 2 X X 2 0 2 X+2 X+2 X+2 0 X X+2 X+2 0 X+2 X+2 2 2 0 0 2 2 X+2 0 X+2 X+2 2 X+2 2 X+2 X 2 X 0 0 X X+2 0 X X+2 X X+2 X X+2 0 0 X 0 2 X X+2 X+2 2 X 2 0 2 2 X X 2 2 2 0 0 0 X X X X+2 0 0 2 X X+2 0 0 0 0 X 0 X X X 0 2 0 X X+2 X+2 X 2 2 0 0 0 2 2 X+2 X X+2 X X 0 X 2 X+2 X+2 X+2 X X+2 X+2 X+2 X X 0 2 X+2 0 X+2 X 2 X+2 X 0 X+2 0 X 0 0 X X X 0 2 0 X+2 0 2 2 X X 2 0 X X 2 X X 2 X+2 0 X+2 2 2 X X+2 X X+2 X+2 0 0 X 0 0 0 0 X X 2 X+2 X 2 X 0 X 0 X X X+2 X+2 0 2 X X 2 0 2 X+2 X+2 0 X 0 2 X X+2 X X+2 X+2 2 0 2 0 X 0 2 X 2 2 0 X 0 X+2 2 0 X+2 X+2 2 2 X+2 0 X 2 X+2 X+2 0 X 0 0 0 X X+2 X+2 X+2 2 X+2 0 0 X X+2 2 X X 0 X X+2 2 X 2 X+2 0 0 0 0 0 2 2 2 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 2 0 2 2 2 2 0 0 0 2 2 2 0 0 0 2 0 0 2 2 0 0 0 2 2 2 2 0 0 2 0 2 2 0 0 0 0 2 0 0 0 0 0 2 2 0 2 2 2 0 0 0 0 0 0 0 2 2 0 2 0 2 generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+127x^78+40x^79+269x^80+52x^81+414x^82+124x^83+385x^84+180x^85+467x^86+208x^87+432x^88+208x^89+329x^90+124x^91+200x^92+68x^93+158x^94+16x^95+119x^96+4x^97+77x^98+50x^100+28x^102+15x^104+1x^124 The gray image is a code over GF(2) with n=348, k=12 and d=156. This code was found by Heurico 1.16 in 2.12 seconds.