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  2  X  2  2  X  X  X  0  1  1  1  1  X  2  0  0  X  X  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 X+2  X X+2  X X+2  2  2  2  2  2  0  2  X  X  2  2  0  X X+2  2  2  X  0  2  X  2  0  0  X  X  2  0
 0  0  X  0  0  0  0  0  0  0 X+2  2  X  X  X  X  0  X  0 X+2 X+2  2  X  2 X+2 X+2  X X+2  0  X  2  2 X+2  2 X+2  0  2  2  2  0  2  X X+2 X+2  X X+2  0  X  X  X X+2  0  0
 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  2  2  X  X X+2  X  X  X  0  0 X+2  2  2  0  X  X  0  X X+2  0  0  X X+2 X+2  0 X+2  X  X X+2  2  X  0
 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  0  0  2 X+2  0 X+2 X+2  X  2  0 X+2 X+2  0  X  0  X X+2 X+2  0  0 X+2  2  0 X+2  2 X+2  2  2  2  0  0
 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  0 X+2 X+2 X+2  2  2 X+2 X+2 X+2  2  X  2  X X+2  X X+2  0 X+2 X+2  0  0 X+2  X  0  X X+2  0  2  0  0
 0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  0  2  0  2  0  0  2  0  0  0  2  0  0  2  0  2  0  2  0  2  0  0  2  0  2  2  2  2  0  2  0  0  0  0  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+65x^42+100x^43+231x^44+278x^45+325x^46+516x^47+628x^48+884x^49+1146x^50+1456x^51+1696x^52+1736x^53+1748x^54+1460x^55+1136x^56+932x^57+621x^58+464x^59+295x^60+226x^61+170x^62+88x^63+99x^64+40x^65+16x^66+12x^67+10x^68+4x^70+1x^78

The gray image is a code over GF(2) with n=212, k=14 and d=84.
This code was found by Heurico 1.16 in 15.1 seconds.