The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+59x^42+294x^43+881x^44+1538x^45+2654x^46+4070x^47+5780x^48+7572x^49+9956x^50+11994x^51+13424x^52+14032x^53+13382x^54+12670x^55+10068x^56+8042x^57+6015x^58+3628x^59+2367x^60+1252x^61+714x^62+356x^63+173x^64+74x^65+50x^66+12x^67+8x^68+2x^69+2x^70+2x^72

The gray image is a code over GF(2) with n=212, k=17 and d=84.
This code was found by Heurico 1.13 in 166 seconds.