The generator matrix

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

generates a code of length 45 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+224x^39+1501x^40+3076x^41+5093x^42+7376x^43+9830x^44+11280x^45+10166x^46+7542x^47+4988x^48+2452x^49+1307x^50+502x^51+128x^52+56x^53+8x^54+2x^55+2x^58+2x^59

The gray image is a code over GF(2) with n=360, k=16 and d=156.
This code was found by Heurico 1.16 in 24.4 seconds.