The generator matrix

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

generates a code of length 45 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+186x^40+764x^41+1656x^42+1880x^43+2549x^44+2566x^45+2539x^46+1946x^47+1229x^48+522x^49+356x^50+108x^51+41x^52+18x^53+7x^54+2x^55+10x^56+2x^57+2x^58

The gray image is a code over GF(2) with n=360, k=14 and d=160.
This code was found by Heurico 1.16 in 1.66 seconds.