The generator matrix

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

generates a code of length 51 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+64x^46+54x^47+131x^48+30x^49+261x^50+988x^51+278x^52+28x^53+72x^54+46x^55+68x^56+6x^57+18x^58+2x^60+1x^98

The gray image is a code over GF(2) with n=408, k=11 and d=184.
This code was found by Heurico 1.16 in 0.172 seconds.