The generator matrix

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

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+19x^44+72x^45+138x^46+292x^47+380x^48+486x^49+673x^50+840x^51+863x^52+834x^53+900x^54+664x^55+633x^56+572x^57+280x^58+232x^59+123x^60+68x^61+48x^62+20x^63+23x^64+14x^65+7x^66+3x^68+2x^69+2x^70+3x^72

The gray image is a code over GF(2) with n=212, k=13 and d=88.
This code was found by Heurico 1.16 in 3.06 seconds.