The generator matrix

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

generates a code of length 52 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+540x^49+789x^50+732x^51+547x^52+508x^53+296x^54+276x^55+162x^56+136x^57+57x^58+48x^59+2x^62+1x^64+1x^68

The gray image is a code over GF(2) with n=416, k=12 and d=196.
This code was found by Heurico 1.16 in 25.1 seconds.