The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+79x^40+144x^41+306x^42+616x^43+451x^44+936x^45+457x^46+584x^47+291x^48+136x^49+61x^50+16x^51+8x^52+5x^54+1x^56+1x^58+1x^60+2x^62

The gray image is a code over GF(2) with n=360, k=12 and d=160.
This code was found by Heurico 1.16 in 0.172 seconds.