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 1 1 1 1 1 1 1 1 0 X X X X 0 2 X 1 1 1 1
0 X 0 0 0 0 0 0 0 0 2 X X X+2 0 X+2 X+2 0 X X X+2 2 0 X X+2 X 2 X 2 X+2 2 X X+2 X+2 X+2 X+2 X+2 X 2 X+2 2 X 2 0 X X X 0 2 0 X+2 X+2
0 0 X 0 0 0 0 0 0 0 X+2 2 X X X X 0 X 0 X+2 X+2 X X+2 X 2 X+2 X 2 2 X+2 0 0 0 2 X+2 X 2 X X+2 2 X 2 X+2 X X+2 X+2 0 0 2 X+2 2 X+2
0 0 0 X 0 0 0 X X+2 X X X+2 0 X 2 0 X+2 X+2 X+2 2 X+2 0 2 2 0 X 0 2 0 X X X+2 X 2 0 X 0 X+2 X+2 X+2 0 X+2 X+2 2 X+2 0 X+2 X+2 X X 2 X
0 0 0 0 X 0 X X X 2 X X X 2 2 X+2 X+2 2 2 0 X+2 X+2 X 0 2 2 X+2 2 X X+2 0 0 2 X+2 0 X 2 2 X X X X+2 X+2 0 2 X+2 X X X 0 2 2
0 0 0 0 0 X X 2 X+2 X+2 X X X+2 0 X 2 2 2 X+2 2 X+2 0 X+2 X+2 X+2 X+2 0 2 2 2 X 0 2 X 2 0 X+2 2 X X X+2 X+2 X+2 X X 2 2 X X+2 X+2 0 X
0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 0 2 0 0 0 0 0 2 2 2 0 0 2 0 2 2 2 2 2 2 0 2 0 0 0 2 0 2 0 2 2 2 2
generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+214x^42+499x^44+824x^46+80x^47+1175x^48+528x^49+2120x^50+1440x^51+2682x^52+1440x^53+2078x^54+528x^55+1251x^56+80x^57+708x^58+457x^60+194x^62+76x^64+6x^66+2x^68+1x^88
The gray image is a code over GF(2) with n=208, k=14 and d=84.
This code was found by Heurico 1.16 in 15.4 seconds.