The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+188x^82+714x^83+1606x^84+1260x^85+2321x^86+1634x^87+2178x^88+1326x^89+1726x^90+942x^91+1024x^92+450x^93+454x^94+242x^95+173x^96+58x^97+42x^98+16x^99+6x^100+10x^101+5x^102+4x^103+4x^104

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 4.53 seconds.