The generator matrix

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

generates a code of length 92 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+195x^84+296x^85+515x^86+510x^87+662x^88+570x^89+695x^90+540x^91+730x^92+552x^93+608x^94+430x^95+478x^96+238x^97+392x^98+246x^99+148x^100+116x^101+107x^102+52x^103+47x^104+14x^105+13x^106+14x^107+7x^108+4x^109+6x^110+4x^112+2x^113

The gray image is a code over GF(2) with n=368, k=13 and d=168.
This code was found by Heurico 1.16 in 6.11 seconds.