The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+332x^91+652x^92+1056x^93+1133x^94+1000x^95+887x^96+808x^97+522x^98+536x^99+397x^100+340x^101+162x^102+136x^103+88x^104+60x^105+53x^106+20x^107+5x^108+1x^110+1x^114+2x^116

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 1.66 seconds.