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

generates a code of length 97 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+156x^89+1040x^90+2234x^91+3326x^92+4722x^93+5418x^94+6202x^95+6721x^96+6900x^97+6782x^98+5890x^99+5305x^100+3946x^101+2899x^102+1936x^103+966x^104+606x^105+228x^106+128x^107+59x^108+28x^109+17x^110+10x^111+2x^112+10x^113+4x^116

The gray image is a code over GF(2) with n=776, k=16 and d=356.
This code was found by Heurico 1.16 in 63.9 seconds.