The generator matrix

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

generates a code of length 90 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+184x^82+244x^83+529x^84+456x^85+680x^86+628x^87+708x^88+580x^89+720x^90+548x^91+669x^92+464x^93+414x^94+312x^95+282x^96+188x^97+186x^98+112x^99+142x^100+32x^101+44x^102+12x^103+31x^104+8x^105+10x^106+4x^108+2x^110+2x^112

The gray image is a code over GF(2) with n=360, k=13 and d=164.
This code was found by Heurico 1.16 in 5.59 seconds.