The generator matrix

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

generates a code of length 51 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+408x^45+1743x^46+3690x^47+5192x^48+7618x^49+8872x^50+10398x^51+9147x^52+8020x^53+5164x^54+2904x^55+1443x^56+642x^57+156x^58+94x^59+19x^60+16x^61+1x^62+2x^63+4x^64+2x^68

The gray image is a code over GF(2) with n=408, k=16 and d=180.
This code was found by Heurico 1.16 in 27.3 seconds.