The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+104x^88+990x^89+2452x^90+3270x^91+4343x^92+5328x^93+6402x^94+6716x^95+7459x^96+6430x^97+6620x^98+4734x^99+3944x^100+2800x^101+1735x^102+1100x^103+538x^104+300x^105+142x^106+40x^107+38x^108+20x^109+9x^110+12x^111+4x^112+4x^113+1x^116

The gray image is a code over GF(2) with n=768, k=16 and d=352.
This code was found by Heurico 1.16 in 61.9 seconds.