The generator matrix

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

generates a code of length 96 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+105x^84+248x^86+16x^87+405x^88+76x^89+507x^90+204x^91+637x^92+296x^93+815x^94+408x^95+870x^96+480x^97+826x^98+304x^99+613x^100+152x^101+392x^102+88x^103+274x^104+20x^105+182x^106+4x^107+125x^108+76x^110+33x^112+18x^114+6x^116+4x^118+3x^122+2x^124+1x^126+1x^136

The gray image is a code over GF(2) with n=384, k=13 and d=168.
This code was found by Heurico 1.16 in 10.2 seconds.