The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+234x^92+754x^93+674x^94+556x^95+382x^96+358x^97+248x^98+264x^99+204x^100+156x^101+82x^102+96x^103+40x^104+24x^105+18x^106+3x^108+1x^110+1x^122

The gray image is a code over GF(2) with n=768, k=12 and d=368.
This code was found by Heurico 1.16 in 0.687 seconds.