The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  1  2  1  2  0  2  2  1  2  1  2  0  0  1  1  0  1  1  1  0  1  1 X+2 X+2 X+2 X+2  1  1  1  X  1  1 X+2  0  1  1 X+2  X X+2 X+2  1  1  2  X  0  1 X+2  1  X  1  1  1  1  1  1  1 X+2 X+2  1  1  2  1 X+2 X+2  1  1  X  1  2  0  1  1  1 X+2  X  0  1  0  1
 0  1  0  0  0  2  2  2  1 X+3 X+1 X+3  1 X+1  1  1  1  0  2  2 X+3  1  1  X X+2  3  1  1  X  3 X+2 X+2 X+1  1  1  2  X  0 X+3  1  1  1  3  1  1 X+2  X  2  1  1 X+2 X+3  1  1  2  1  X  1  3  1 X+2 X+1  0  3 X+2  3 X+2  1  0  2 X+1  1 X+1 X+2  X X+3  X  0 X+1  X  1 X+3  3  0  1  X  1  0  1  1
 0  0  1  0  2  1  3  1 X+1  1  2  3 X+1  0  0  2 X+3  1  0  1  2  2 X+3  X X+2 X+1 X+2  2 X+3 X+3  1  1  X  0  3  X  1 X+2 X+2 X+2  X  3  3  1  3  2  3  1  0  X  1 X+1 X+2  3  0  3 X+2  2 X+2 X+3 X+1 X+3 X+3 X+1  1 X+3  0 X+3  1 X+2 X+1  1  0  0 X+2 X+2 X+1  0 X+2  X X+3 X+3  0 X+1  0  2 X+2  3  X  1
 0  0  0  1 X+3 X+3  0 X+1  2  0  2 X+3  1 X+1  3  X X+1  X X+2  1  X X+3 X+2  1  3  0  3 X+1  1 X+1  1  2  X  X X+3  1  2  X X+1  0  X  2  1  0 X+1 X+2  X  2  2 X+1 X+3 X+2 X+2  2  1  1 X+1 X+3 X+3 X+1  0 X+1  2  2  1  3  2  3  1  3  3 X+3  X  1  1  0  X  1  1  1  3  2  1  1  3  1 X+1  X X+2  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+366x^84+882x^86+742x^88+672x^90+510x^92+368x^94+194x^96+152x^98+112x^100+54x^102+22x^104+16x^106+4x^108+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 1.16 in 3.39 seconds.