The generator matrix

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

generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+60x^44+186x^45+317x^46+526x^47+811x^48+1084x^49+1241x^50+1462x^51+1694x^52+1666x^53+1685x^54+1574x^55+1307x^56+1006x^57+629x^58+478x^59+317x^60+140x^61+82x^62+52x^63+29x^64+14x^65+14x^66+4x^67+5x^68

The gray image is a code over GF(2) with n=212, k=14 and d=88.
This code was found by Heurico 1.16 in 9.65 seconds.