The generator matrix

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

generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+180x^84+702x^85+700x^86+628x^87+446x^88+402x^89+249x^90+220x^91+170x^92+116x^93+88x^94+84x^95+32x^96+56x^97+16x^98+1x^100+3x^102+2x^104

The gray image is a code over GF(2) with n=704, k=12 and d=336.
This code was found by Heurico 1.16 in 0.484 seconds.