The generator matrix

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

generates a code of length 90 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+318x^84+188x^85+574x^86+252x^87+605x^88+156x^89+480x^90+144x^91+402x^92+112x^93+274x^94+60x^95+142x^96+56x^97+120x^98+8x^99+84x^100+20x^101+44x^102+16x^103+15x^104+12x^105+12x^106+1x^112

The gray image is a code over GF(2) with n=360, k=12 and d=168.
This code was found by Heurico 1.11 in 1.02 seconds.