The generator matrix

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

generates a code of length 90 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+87x^80+44x^81+272x^82+228x^83+384x^84+508x^85+520x^86+504x^87+561x^88+800x^89+591x^90+680x^91+544x^92+688x^93+457x^94+320x^95+329x^96+244x^97+149x^98+52x^99+97x^100+20x^101+36x^102+8x^103+27x^104+11x^106+13x^108+11x^110+3x^112+1x^114+1x^116+1x^124

The gray image is a code over GF(2) with n=360, k=13 and d=160.
This code was found by Heurico 1.16 in 6.56 seconds.