The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+336x^84+40x^85+106x^86+232x^87+666x^88+200x^89+108x^90+24x^91+276x^92+16x^93+40x^94+2x^110+1x^128

The gray image is a code over GF(2) with n=704, k=11 and d=336.
This code was found by Heurico 1.16 in 0.563 seconds.