The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X X+2  1  1  0  1  1 X+2  1  1  2  0  1  1  X  1  1  X  1  1  0  1  1  X  X  1  1  1  1  2  X  1  1  0  0  1  1  1  1  1  2  1  X  0  1  1  0  2  1  0  0  1  1  0  X  1  1  1  X  X  1  1  1  1  1  X  1  1  1  X X+2  1  2  1  2  X
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1 X+2  1  1  1  X  3  1  0 X+1  1 X+2 X+1 X+2  1  X  1  1  1  1  X  1  2  1  0 X+3  1  1 X+3  2  0  3  1  1 X+1 X+2  1  1 X+2  3 X+3  0  2  1 X+1 X+2  1 X+2  0  1 X+2  0  1  1  3  3  1  2  1 X+2  1  X  1 X+3 X+2 X+3 X+3  0  1  X  3  0  1  1  0  1  0  1  1
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  1  0  1 X+1  X  0 X+2  2  1 X+3  3 X+2  0 X+3  1 X+2 X+1  X  1  2  1  1  X  1 X+1  2  2  0 X+1  0  1 X+2 X+3 X+2 X+1 X+1  2  2  1 X+1  X  2 X+3 X+2 X+1  1  1  1  0 X+2 X+1  1  3  3 X+2  2  X X+3  1  3  X X+1  1  2  0  2 X+1 X+2 X+3  3  1  1  2  X X+1 X+3  2 X+2 X+2  1
 0  0  0  2  0  0  0  0  2  2  0  0  0  2  2  0  2  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  2  0  2  2  2  0  0  0  0  0  2  2  2  2  0  2  0  0  0  0  2  2  0  2  2  0  2  0  2  0  2  0  2  2  0  2  2  2  0  0  0  2  2  2  0  0  0  0  0  2  2  0  2  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0  2  2  2  2  0  2  0  0  2  0  0  0  2  2  2  0  0  2  0  0  0  0  0  2  0  2  2  0  0  0  2  0  2  0  2  0  2  2  0  2  2  2  2  0  2  2  0  2  0  0  2  0  0  0  0  2  0  2  2  0  2  0  2  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  0  0  2  2  0  0  2  0  0  2  2  2  0  2  2  2  0  2  2  0  0  2  2  2  0  2  0  2  2  2  2  2  0  0  2  2  0  2  2  2  0  0  2  2  0  0  2  0  2  2  2  0  2  2  2  0  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  0  2  2  2  0  0  2  2  2  2  0  0  2  2  2  0  2  2  0  2  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  2  2  2  0  0  0  2  0  0  0  0  2  2  2  0  0  0  2  2  2  2  2  2  0  0  2  0  0  2  0  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0  0  0  0  0  2  2  2  0  0  2  2  0  0  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  2  2  0  0  0  0  2  0  0  2  2  2  2  2  0  2  2  2  0  0  2  2  2  2  0  0  2  2  0  2  0  2  0  0  0  2  2  0  2  2  2  2  2  2  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+102x^80+206x^81+404x^82+628x^83+711x^84+976x^85+1125x^86+1158x^87+1273x^88+1206x^89+1141x^90+1212x^91+1207x^92+1110x^93+1028x^94+840x^95+667x^96+504x^97+322x^98+230x^99+107x^100+82x^101+51x^102+24x^103+19x^104+12x^105+20x^106+2x^107+7x^108+4x^110+2x^111+2x^112+1x^122

The gray image is a code over GF(2) with n=360, k=14 and d=160.
This code was found by Heurico 1.16 in 20.6 seconds.