The generator matrix

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

generates a code of length 92 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+40x^82+100x^83+198x^84+238x^85+466x^86+468x^87+457x^88+702x^89+584x^90+608x^91+693x^92+586x^93+597x^94+644x^95+396x^96+418x^97+419x^98+178x^99+137x^100+80x^101+37x^102+28x^103+19x^104+12x^105+22x^106+16x^107+14x^108+8x^109+7x^110+4x^111+2x^112+4x^113+2x^114+2x^115+2x^116+1x^120+1x^122+1x^126

The gray image is a code over GF(2) with n=368, k=13 and d=164.
This code was found by Heurico 1.16 in 7.46 seconds.