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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+76x^88+178x^89+300x^90+148x^91+75x^92+76x^93+79x^94+36x^95+23x^96+10x^97+19x^98+1x^100+1x^102+1x^130

The gray image is a code over GF(2) with n=728, k=10 and d=352.
This code was found by Heurico 1.16 in 0.578 seconds.