The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+290x^89+982x^90+1780x^91+2270x^92+2984x^93+3335x^94+3672x^95+3454x^96+3142x^97+3076x^98+2698x^99+1816x^100+1390x^101+807x^102+508x^103+265x^104+104x^105+78x^106+54x^107+32x^108+10x^109+4x^110+4x^111+2x^112+6x^114+4x^119

The gray image is a code over GF(2) with n=768, k=15 and d=356.
This code was found by Heurico 1.16 in 17.6 seconds.