The generator matrix

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

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+279x^50+410x^51+270x^52+196x^53+245x^54+366x^55+234x^56+16x^57+12x^58+4x^59+4x^60+8x^62+2x^68+1x^76

The gray image is a code over GF(2) with n=424, k=11 and d=200.
This code was found by Heurico 1.16 in 0.094 seconds.