The generator matrix

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

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+138x^84+310x^85+542x^86+476x^87+692x^88+624x^89+766x^90+522x^91+713x^92+492x^93+557x^94+424x^95+459x^96+308x^97+363x^98+228x^99+202x^100+126x^101+109x^102+44x^103+28x^104+20x^105+23x^106+2x^107+7x^108+8x^109+8x^110

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 4.54 seconds.