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  1  2  X  1  X  X  1  X  1  1  1  1  0  1  X  2  X  1  1  1  X  1  X  1  X  1  0  1  1  1  X  1  1  2  0  1  0  1  1  2  2  1  2  1  X  0  1  0  1  1  X  1  X  1  2  X  1
 0  X  0  0  0  X X+2  X  0  2  2  X X+2  X  X  0  0  0  2 X+2 X+2  2 X+2 X+2  0  X  0  X  2  0  X  X X+2  X  X  0  2  0  X  0  X X+2 X+2  X  X X+2  2  X  2  0  0  X  2  0  2  2  X  0  X  0  0 X+2  X  2  0  2  2  X  X X+2  0 X+2  X  0  X  0  2  2  2  2  0  0  2  X  X  2  X  2 X+2  X  0  X  0  0  2  0
 0  0  X  0  X  X X+2  0  0  0  X  X  X  0  2 X+2  X  0  2  2  0  0 X+2  X X+2  2  2 X+2  X  X  0 X+2  2  0  0  0 X+2  0 X+2  X  X X+2  2 X+2  2  X  X  0  2  2 X+2  X  2 X+2  X  X X+2 X+2  2  2  X  0  X X+2 X+2  0  2  2 X+2  2  X  X X+2  X  0  X  X  X  X  X  X  X  X  X  X  0 X+2  X X+2  0 X+2  X  2  X  2  0
 0  0  0  X  X  0 X+2  X  2  X  2  0  X  2 X+2  X  2  2  X X+2  2  X  0 X+2 X+2  X  0  2  2 X+2  2  X  2  0 X+2  0  X  X  X  2  2  X  X  0  X  2  0  0  0  X  0  X  0  0 X+2 X+2  X  X X+2  X  2  2  X X+2 X+2  X  X  0  0 X+2  X  0  0  X  2  X  0  2  0  X  X  0  2  X  2 X+2  X  2  0 X+2  0 X+2  X X+2 X+2  0
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0  0  2  2  2  2  0  2  2  0  2  2  0  0  2  0  2  2  2  2  0  2  0  0  2  0  2  0  2  0  2  2  2  2  2  0  2  2  0  0  2  0  2  0  2  0  2  2  0  2  2  0  0  0  0  2  2  2  2  0  2  2  0  2  2  2  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  2  2  0  0  0  0  0  2  0  0  2  0  2  2  0  0  2  2  2  2  2  2  2  2  0  2  0  0  0  0  0  2  0  0  0  2  2  0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  0  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  0  2  2  0  0  0  2  2  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  2  0  0  2  0  2  2  2  0  2  0  0  0  2  2  0  2  0  2  2  0  2  0  2  2  0  2  0  0  0  0  0  0  2  0  2  0  0  2  0  2  0  0  2  2  2  0  2  2  2  0  2  0  2  2  2  2  0  0  2  2  0  0  2  2  0  0  0  0  2  0  2  2  0  0  0  0  0  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  0  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  2  0  0  2  2  0  2  2  0  0  2  0  0  0  2  0  2  2  2  2  2  0  2  0  0  2  2  2  0  0  0  0  2  0  2  2  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+37x^84+72x^85+117x^86+186x^87+254x^88+304x^89+341x^90+370x^91+454x^92+520x^93+610x^94+644x^95+630x^96+628x^97+546x^98+530x^99+404x^100+350x^101+286x^102+216x^103+180x^104+116x^105+100x^106+66x^107+61x^108+48x^109+34x^110+24x^111+23x^112+8x^113+12x^114+10x^115+1x^116+2x^117+1x^118+2x^119+3x^124+1x^138

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 9.82 seconds.