The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+184x^91+952x^92+928x^93+1076x^94+988x^95+1020x^96+624x^97+716x^98+396x^99+466x^100+272x^101+216x^102+128x^103+100x^104+52x^105+48x^106+10x^108+12x^109+2x^116+1x^120

The gray image is a code over GF(2) with n=768, k=13 and d=364.
This code was found by Heurico 1.16 in 1.72 seconds.