The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  1  0  1  1 X+2  1  1  2  1  1  1  1  X  1  0  1  1  1  1  X  X  1  1  1  1  X  1  1  0  X  0  1  X  0  1 X+2 X+2  1  0  0
 0  1  1  0 X+3  1  X X+1  1  3  1 X+2 X+3  0  1 X+2  1  1  2  3  1  1  X X+1  3  1  X  1  X  0 X+1 X+3  1  1  3  X  0 X+2  1  0 X+2  X  1  1 X+2  1  1  3  1  1  1  X  1
 0  0  X  0 X+2  0  0  X  0 X+2  0  0  0  X X+2  X  2  X  X  2  X  X  2  X  2  X X+2  2  0  2  2  X X+2  0  2  0  X  0 X+2  0  0  0  0  2  2 X+2  X  2  2  X  0  2 X+2
 0  0  0  X  0  0  X  X  X  X X+2  2  X  X X+2  X X+2  X  2  2  0 X+2 X+2  0  2  2  2  2  2  0  0  0  2  0  0 X+2  X  2 X+2  2  0 X+2  X  0 X+2  X  2  0  X  0  0  X X+2
 0  0  0  0  2  0  0  0  0  0  2  2  0  2  0  2  2  0  2  0  2  2  2  0  2  0  2  0  2  0  2  0  2  2  0  0  0  0  2  0  2  0  2  0  0  2  0  0  0  0  2  0  2
 0  0  0  0  0  2  0  0  2  2  2  0  0  0  2  2  2  0  2  0  2  2  0  0  2  0  0  0  2  2  0  2  0  2  2  2  2  0  2  0  0  0  0  2  2  2  0  2  0  2  2  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  0  2  2  2  0  2  0  2  2  0  2  0  2  2  0  0  2  0  0  0  0  0  0
 0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  2  2  0  2  0  0  0  2  2  0  0  2  2  0  2  2  2  0  0  0  0  0  0  2  0  0  0  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+188x^44+40x^45+492x^46+276x^47+999x^48+592x^49+1546x^50+1392x^51+1911x^52+1552x^53+1948x^54+1384x^55+1613x^56+592x^57+840x^58+272x^59+442x^60+40x^61+152x^62+4x^63+80x^64+14x^66+11x^68+3x^72

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 11.2 seconds.