The generator matrix

 1  0  0  1  1  1 X^2+X X^2+2  1  1  0  1  1 X^2 X^2  1 X^2+2  1  1 X^2+2 X^2+X  1  X  1  1  1  1  2 X^2+X  1  1  X  1  1  1 X+2  1 X+2 X^2+X+2  1  X  X X^2+X  1  1
 0  1  0  0  1 X+3  1  1 X^2+1  X  1 X^2+2 X+1 X^2  1 X+3  1 X^2 X^2+X+3  1  0 X^2+X+2  1 X+2 X^2+X+2  3 X^2+3 X+2  1 X^2 X^2+X+1 X^2+X X^2+1 X^2+3  0  2  1  1  1 X+1  1 X^2+2  1 X^2+X+3  2
 0  0  1  1  1 X^2+X  1  3  X  3  0  2 X^2+1  1  3 X+2  X X+2 X+3 X^2+X+2  1 X+1  1 X^2+2  3 X+1 X^2+X  1 X^2+X+3  X X^2+X+1  1  2  2 X^2+X+3  1 X^2+2 X^2+X+1  2 X^2+X+1 X^2+2 X^2+2 X^2+1 X^2+1  0
 0  0  0  X  2 X+2 X+2 X^2+2 X^2 X^2 X^2+X X^2+X+2 X^2+X X^2+X X+2  0  2 X^2+2 X+2 X^2+X+2  2  2 X^2 X^2+X+2 X^2+X+2  X X+2 X+2 X^2 X^2+X+2 X^2  2 X^2+2 X+2 X^2+2 X^2+X+2 X^2+X X^2+X+2 X^2+X+2  0  2 X+2  2  2 X^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+72x^39+814x^40+1384x^41+2776x^42+3816x^43+4965x^44+5244x^45+5111x^46+3678x^47+2709x^48+1208x^49+646x^50+156x^51+117x^52+52x^53+11x^54+6x^55+2x^56

The gray image is a code over GF(2) with n=360, k=15 and d=156.
This code was found by Heurico 1.16 in 6.09 seconds.