The generator matrix

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

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+174x^47+890x^48+1822x^49+2793x^50+4072x^51+3998x^52+5130x^53+4751x^54+3922x^55+2411x^56+1466x^57+747x^58+388x^59+112x^60+38x^61+37x^62+4x^63+4x^64+8x^65

The gray image is a code over GF(2) with n=424, k=15 and d=188.
This code was found by Heurico 1.16 in 7.52 seconds.