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

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+92x^89+248x^90+124x^91+206x^92+100x^93+120x^94+40x^95+46x^96+16x^97+12x^98+8x^99+2x^100+4x^102+4x^103+1x^128

The gray image is a code over GF(2) with n=736, k=10 and d=356.
This code was found by Heurico 1.16 in 0.593 seconds.