The generator matrix

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

generates a code of length 92 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+192x^83+479x^84+620x^85+910x^86+1052x^87+962x^88+1236x^89+1259x^90+1144x^91+1255x^92+1226x^93+1088x^94+946x^95+982x^96+766x^97+596x^98+620x^99+394x^100+244x^101+190x^102+94x^103+47x^104+34x^105+13x^106+16x^107+8x^108+2x^109+8x^110

The gray image is a code over GF(2) with n=368, k=14 and d=166.
This code was found by Heurico 1.16 in 18.1 seconds.