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

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+354x^88+360x^89+354x^90+180x^91+257x^92+216x^93+146x^94+52x^95+60x^96+24x^97+24x^98+8x^100+6x^104+4x^106+1x^124+1x^128

The gray image is a code over GF(2) with n=728, k=11 and d=352.
This code was found by Heurico 1.16 in 2.95 seconds.