The generator matrix

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

generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+352x^85+327x^86+360x^87+188x^88+250x^89+233x^90+196x^91+46x^92+70x^93+4x^95+2x^96+4x^97+4x^99+1x^100+4x^101+4x^105+1x^112+1x^128

The gray image is a code over GF(2) with n=704, k=11 and d=340.
This code was found by Heurico 1.16 in 35.8 seconds.