The generator matrix

 1  0  0  1  1  1 X^2  1 X^2+X+2  1  1  1  0  0  1 X^2+X  1  1 X^2  1  X X+2 X+2  1  1  1  1  2  1  1 X^2+X  1 X^2+2 X^2+X+2  0 X+2  1  1  1  1  1 X+2  1  1  0 X^2 X^2+X+2  1  1 X^2  1
 0  1  0  0 X^2+1 X+3  1 X^2+X X^2+X X^2+X+1 X^2+3 X^2+X+2  1  1 X^2+X+2  1 X+3 X^2+1 X+2  X  1 X^2+2  1 X+2 X^2+X X^2 X+1  1 X^2+X+1 X+3  0 X^2+2  1  X  X  1 X^2 X^2+2  3 X^2+1 X^2+2  1 X^2+1  3  1 X+2  1 X+2 X+1  0  0
 0  0  1  1  1 X^2 X^2+X+1  3  1 X^2+X  1 X^2+X  X  1 X^2+3  0  1 X^2  1 X^2+2 X^2+1  1 X+1 X^2+X X+3  X X^2+X+1 X^2+2  X X+1  1  0 X^2+X+1  1  1 X^2+1 X^2+1  X X^2+2 X^2+X+1  3  3 X^2+X+1  X X^2  1  0 X+1 X+3  1  0
 0  0  0  X X+2  2 X^2+X  X X+2 X+2  2 X^2+X X+2 X^2  2 X^2+2 X^2+X+2 X^2 X^2+X X^2+X X^2  2  X  0  0 X^2  0  X X^2+X X^2+X X^2+2  X X^2 X^2+X  2 X^2+X X^2+X+2  0 X+2  2 X^2  0 X+2 X^2+2 X+2 X^2  2 X^2+2 X+2 X^2+X+2  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+158x^45+775x^46+1846x^47+2571x^48+3986x^49+4573x^50+5294x^51+4663x^52+3758x^53+2361x^54+1622x^55+612x^56+310x^57+151x^58+34x^59+31x^60+12x^61+4x^62+4x^63+2x^64

The gray image is a code over GF(2) with n=408, k=15 and d=180.
This code was found by Heurico 1.16 in 7.16 seconds.