The generator matrix

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

generates a code of length 45 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+402x^40+858x^42+947x^44+796x^46+594x^48+314x^50+125x^52+48x^54+11x^56

The gray image is a code over GF(2) with n=180, k=12 and d=80.
This code was found by Heurico 1.16 in 2.81 seconds.