The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+36x^42+156x^43+73x^44+80x^45+45x^46+24x^47+17x^48+48x^49+14x^50+12x^51+5x^52+1x^70

The gray image is a code over GF(2) with n=180, k=9 and d=84.
This code was found by Heurico 1.13 in 0.031 seconds.