The generator matrix

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

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+42x^42+92x^43+269x^44+376x^45+541x^46+742x^47+966x^48+1262x^49+1447x^50+1662x^51+1697x^52+1722x^53+1409x^54+1132x^55+1007x^56+690x^57+507x^58+364x^59+198x^60+94x^61+78x^62+38x^63+22x^64+16x^65+8x^66+2x^67

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 10.7 seconds.