The generator matrix

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

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+634x^84+104x^85+940x^86+176x^87+689x^88+128x^89+700x^90+80x^91+450x^92+24x^93+108x^94+27x^96+12x^98+20x^100+2x^112+1x^120

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 40.8 seconds.