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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+4x^90+88x^91+6x^92+24x^93+2x^94+1x^96+2x^106

The gray image is a code over GF(2) with n=728, k=7 and d=360.
This code was found by Heurico 1.16 in 0.547 seconds.