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 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 X 1 1 0 1 X X 1 2 1 1 X 1 X 1 2 1 1 2 X 1 X 0 1 0 X 0 0 0 X X+2 X 2 0 X+2 2 X X X 0 X+2 X X+2 X 0 0 2 0 X+2 0 X 2 X X+2 0 0 2 2 X X+2 2 2 X 0 X 2 2 X 0 X 2 X+2 X 2 X+2 X+2 X X+2 2 0 X+2 X 0 2 X+2 X 2 X+2 0 2 0 X+2 X X 2 X+2 X+2 X 0 X X 0 0 2 0 X 0 X X+2 X+2 0 X 0 0 0 X 0 X X X 0 2 0 X+2 X 2 X+2 2 X 2 0 X+2 X+2 2 0 X X+2 2 X+2 X 0 0 X X 0 2 0 X+2 X 0 X 0 X 0 X X+2 2 2 2 0 0 X+2 X+2 X X 0 X 2 X 2 X 2 X X+2 X+2 X X+2 2 X+2 2 0 0 X+2 X+2 2 X 2 2 0 0 0 0 2 X 2 X 2 X+2 X X X 0 0 0 0 X X 0 X X+2 0 X+2 X 2 X 0 2 X X 0 0 X X+2 2 X+2 0 X+2 0 X X 0 2 X+2 0 2 X 2 X 2 X 2 2 0 X+2 X 2 X+2 X X+2 X X+2 0 0 2 X+2 X+2 0 2 2 X 0 2 2 X X X X X 0 X 2 2 X X+2 X 2 X X 0 X X+2 X+2 2 2 0 X+2 0 X+2 0 X 0 0 0 0 0 2 0 0 0 2 2 2 2 0 2 0 0 2 2 2 0 2 2 0 2 2 0 2 0 2 0 2 0 0 2 2 2 0 0 2 2 0 2 0 2 0 0 0 0 0 0 0 2 2 0 2 2 0 2 2 2 0 2 0 2 0 0 2 2 0 0 0 2 2 2 2 2 2 2 0 0 2 0 2 2 0 2 0 2 2 0 0 0 0 0 2 0 2 0 2 2 2 0 2 2 0 2 2 0 2 0 2 2 0 0 2 0 2 0 0 2 2 2 2 0 2 0 2 2 2 2 2 0 2 0 2 2 0 0 2 2 2 0 2 2 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 2 0 0 0 0 0 0 0 2 0 0 0 2 2 2 generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+176x^82+4x^83+192x^84+64x^85+207x^86+104x^87+226x^88+164x^89+270x^90+132x^91+173x^92+24x^93+116x^94+16x^95+66x^96+4x^97+41x^98+34x^100+16x^102+7x^104+5x^106+4x^108+1x^110+1x^148 The gray image is a code over GF(2) with n=356, k=11 and d=164. This code was found by Heurico 1.16 in 83 seconds.