The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+201x^82+806x^83+1278x^84+1654x^85+1952x^86+2016x^87+1796x^88+1878x^89+1223x^90+1156x^91+846x^92+562x^93+388x^94+288x^95+209x^96+66x^97+25x^98+22x^99+12x^100+2x^104+3x^106

The gray image is a code over GF(2) with n=704, k=14 and d=328.
This code was found by Heurico 1.16 in 4.36 seconds.