The generator matrix

 1  0  1  1  1 X+2  1  1  0 X+2  1  1  1  2  1 X+2  1  1  1  X  1  2  1  1 X+2  1  1  1  1  1  X  1  1 X+2  1  1  2  2  1  1  1 X+2  1  1  2  1  2  1  1  1  1  0  2  1  1  1  1  1  2  1  1  1  1  X  1  1  1  0  1  1  1  1  0 X+2  X  1  1  1  X  0  2  0  0  X  X  1  1  1  1  2
 0  1  1  0 X+3  1  X X+1  1  1 X+2  3  2  1  1  1  1  X X+1  1 X+2  1  0 X+1  1  0 X+3  2  1  X  1 X+1 X+2  1  2  3  1  1  2 X+1  X  1  3 X+1  1  3  1 X+3  X X+2 X+2  1  1 X+3  3  2 X+1  1  1  2  3 X+2  2  1  0 X+2  1  1  0  3  1 X+2  1  1 X+2  3  1 X+2  2  1  1  X  1  X  1  1  0  3 X+1  1
 0  0  X  0 X+2  0  0  X X+2  X  2  X  X  X  0  2  2  X  0  X  X  2 X+2  2 X+2 X+2  X X+2  2  2 X+2  2  2  2  0  0  0 X+2  0  X  X X+2  X X+2  2  2 X+2  0 X+2  0 X+2  2  0 X+2  X  2  2  X X+2  2  X  X  X  2 X+2  0  0  X  0  2  0 X+2  0  0 X+2 X+2  X  2  2  X  2 X+2  0 X+2 X+2  X  2  X  2  2
 0  0  0  X  0  0  X  X  X  X  0  X  0  2 X+2 X+2  0  2 X+2  2 X+2  X X+2  2 X+2  X  2  0  X  X  0  2  0  2  2  0 X+2 X+2  X X+2  2 X+2 X+2  0  2 X+2  0 X+2  X  0  0  2  X  X  2  X  2  0  2 X+2  X X+2  X  X  0  X  2  2  2  X  X  0  2 X+2  2  2  0  X  X  X  2  X  0  0  X  0  2  X X+2  X
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  2  2  2  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  0  2  2  2  2  0  0  2  2  0  2  0  0  2  2  0  0  2  0  0  2  2  2  0  2  2  2  0  2  2  0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2
 0  0  0  0  0  2  0  0  0  2  2  0  2  2  0  0  0  0  0  0  2  2  0  0  0  0  0  2  0  2  2  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  2  2  2  0  0  0  0  0  2  2  0  2  2  2  0  2  2  2  0  0  2  2  0  2  0  2  2  0  2  0  0  0  0  0  0  0  0  2  0  2  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  0  2  2  2  0  0  2  2  0  0  2  2  0  2  2  0  2  0  0  0  2  0  2  2  2  2  2  2  2  0  0  2  0  0  2  0  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  2  0  2  0  0
 0  0  0  0  0  0  0  2  2  2  0  2  0  0  2  2  0  0  2  0  2  2  2  2  2  2  2  2  0  0  0  2  2  0  2  2  0  2  0  2  0  0  0  0  0  0  0  2  0  0  2  2  0  2  2  0  0  0  0  2  0  2  0  0  2  0  2  2  2  2  0  0  0  0  2  0  2  2  0  0  2  2  2  0  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 79.

Homogenous weight enumerator: w(x)=1x^0+74x^79+146x^80+296x^81+395x^82+502x^83+696x^84+816x^85+970x^86+1180x^87+1279x^88+1278x^89+1338x^90+1366x^91+1246x^92+1090x^93+988x^94+730x^95+570x^96+462x^97+333x^98+192x^99+113x^100+110x^101+56x^102+38x^103+31x^104+36x^105+14x^106+12x^107+6x^108+8x^109+2x^110+2x^111+5x^112+3x^116

The gray image is a code over GF(2) with n=360, k=14 and d=158.
This code was found by Heurico 1.16 in 47.2 seconds.