The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  2  1  1  1  1 X^2+X  1  1 X+2 X^2+X+2  1 X+2  1  1 X^2+2 X^2  1  1  2  1  1 X^2  1  1  1  1 X+2  1  1  1  1  1  1 X^2+X  2  1  1  2  0 X^2 X^2+2 X+2 X^2  X  X X^2+X+2 X^2  X  0  X  0  0  X X^2+2 X^2+X  1  1  1  1 X^2+X+2  1  0  1  1 X^2  2  2  1  1  X X+2  1  X X^2+2  1  1  0  1  1  1  X  1
 0  1  1 X^2 X+1  1  X X^2+X+1  1  X  1 X^2+X+1 X+1 X^2+1  2  1  1 X^2+2  1  1 X+2  1 X+2 X^2+3  1  1 X+3 X^2  1 X^2+X+3  0  1 X^2+X+1  0 X^2+X X^2+3  1 X^2+3 X^2+X X^2+2  1 X^2+X  3  1  1 X+1 X^2+X+2  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  0 X+2 X^2+X+3 X^2+X+3  1 X^2+3  1 X^2  2  1  1  1 X^2+X+3 X^2+X+2 X^2+2  1 X^2 X^2+X  2 X^2+X+3  3  X X^2+X X+2 X+3 X^2 X+1
 0  0  X X+2  2 X+2 X+2  X X^2+2 X^2 X+2 X^2+2 X^2+X X^2+X X^2  2 X^2+2 X^2+X X^2+X X+2  0 X^2 X^2+X  2  0  X X^2+2 X^2 X^2  0 X^2+X+2 X^2+X+2 X^2+X+2 X+2  2  X  2 X^2+2 X^2  2  0 X^2+X+2 X^2+X+2 X^2+X X^2+X  X X+2  0 X^2+2 X^2  2 X+2 X^2+2 X^2+X  X  2 X+2 X^2  2 X^2+X+2 X^2+X+2 X^2+X  2  X X^2+2 X^2 X+2 X^2+2  X X^2+X+2  0  X  0 X^2+X X^2+X X^2+2  2 X^2+X X^2+X X+2  0 X^2+2 X^2+2  X X^2 X^2+X  X  0  X X+2 X^2+X+2  0

generates a code of length 92 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+422x^89+220x^90+486x^91+90x^92+316x^93+98x^94+256x^95+17x^96+82x^97+14x^98+30x^99+2x^100+4x^102+4x^105+4x^107+2x^124

The gray image is a code over GF(2) with n=736, k=11 and d=356.
This code was found by Heurico 1.16 in 82 seconds.