The generator matrix 1 0 1 1 1 X+2 1 1 0 1 X+2 1 1 1 0 1 1 X+2 2 1 1 X+2 1 1 X+2 1 1 1 1 0 1 1 X+2 0 1 1 1 X 1 1 2 1 1 1 1 X+2 1 X 1 1 0 1 1 0 X 1 1 1 X 1 1 1 1 1 1 1 0 X 1 1 1 1 1 X+2 X+2 X X+2 1 1 2 1 1 X X 1 2 1 0 2 1 1 1 1 2 0 0 0 1 X+1 X+2 1 1 0 X+1 1 3 1 X+2 0 X+1 1 X+2 3 1 1 2 X+1 1 3 X+2 1 0 X+1 3 X+2 1 X X+3 1 1 3 0 X+1 1 X+2 3 1 2 X+1 2 1 1 X+3 1 X+2 3 1 X X+3 1 1 X+2 3 1 X+2 X 0 0 X+2 X X+1 1 1 1 X+3 X+1 0 2 0 1 1 X 1 1 0 1 1 X+1 1 1 0 X 2 1 X X+3 X+3 3 1 X X X 0 0 2 0 0 0 0 0 2 2 2 0 2 0 0 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 0 2 2 2 0 2 2 0 2 2 2 0 0 0 2 0 0 0 2 2 2 2 2 2 2 0 0 2 2 0 0 0 2 0 2 2 0 0 2 2 2 2 0 2 0 0 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 0 0 2 0 0 2 2 2 2 2 0 0 0 0 2 2 0 2 2 0 2 0 0 2 0 0 0 2 2 2 2 2 2 2 0 0 2 0 2 2 2 0 2 0 2 2 0 0 2 2 2 0 0 2 2 0 2 0 0 0 0 2 0 0 2 2 0 2 0 2 2 0 2 0 2 2 2 0 2 2 2 0 2 0 0 0 0 2 2 2 2 2 2 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 0 2 0 0 2 2 2 2 0 2 0 2 0 0 2 0 2 0 2 0 0 0 0 0 0 2 2 0 0 0 0 0 2 2 0 0 2 2 2 0 2 0 0 0 0 0 2 0 2 0 2 2 2 0 2 0 2 0 2 0 0 2 0 2 0 0 2 2 0 2 2 2 0 2 0 2 0 0 2 2 0 2 2 0 2 0 2 2 0 0 0 2 2 2 2 0 0 2 0 0 2 0 2 0 0 0 2 0 2 0 2 2 0 2 2 0 0 2 2 2 0 2 2 0 2 0 2 2 2 0 0 0 0 0 2 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 2 0 2 2 2 0 2 0 2 2 0 2 0 2 2 0 0 2 2 2 0 2 0 0 0 2 2 2 0 0 2 0 0 2 2 0 0 0 0 0 2 2 2 2 2 2 0 0 2 2 2 2 0 0 2 0 0 0 2 2 0 2 0 2 0 0 0 2 0 2 0 0 0 0 0 0 0 0 generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 89. Homogenous weight enumerator: w(x)=1x^0+56x^89+145x^90+170x^91+189x^92+166x^93+128x^94+142x^95+162x^96+138x^97+121x^98+154x^99+119x^100+110x^101+104x^102+42x^103+27x^104+38x^105+10x^106+4x^107+10x^108+4x^109+2x^114+1x^116+1x^120+1x^122+1x^124+1x^128+1x^130 The gray image is a code over GF(2) with n=384, k=11 and d=178. This code was found by Heurico 1.16 in 1.47 seconds.