The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+168x^90+1024x^91+1288x^92+1920x^93+1570x^94+2084x^95+1410x^96+2142x^97+962x^98+1316x^99+752x^100+676x^101+433x^102+292x^103+114x^104+94x^105+53x^106+36x^107+25x^108+16x^109+5x^110+1x^112+1x^114+1x^116

The gray image is a code over GF(2) with n=768, k=14 and d=360.
This code was found by Heurico 1.16 in 5.23 seconds.