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  2  1  1  1  1  2  X  0  0  X  0  X  0  1  1  X  X  X  X  1  0  1  X  1  1
 0  X  0  0  0  X X+2  X  0  2  2  X X+2  X  X  0  0  0  2 X+2 X+2  2  X X+2 X+2  0  0 X+2  2  X  0  X  2  X X+2  2  X  0  0  0  X  0  X  2  2  X X+2  2  2  X  2 X+2  X
 0  0  X  0  X  X X+2  0  0  0  X  X  X  0  2 X+2  X  0  2  2  0  0  2 X+2  X X+2  2 X+2  X  0 X+2  X X+2 X+2  X  X  2 X+2  0  0  0  2  X  0 X+2  2  2  2  0  X  0  2  2
 0  0  0  X  X  0 X+2  X  2  X  2  0  X  2 X+2  X  2  2  X X+2  2  X  X  0 X+2 X+2  0 X+2  X  0  0  0 X+2  0  X  2  0  2  X X+2  0  2  0  X  0  X  X  X  X  0 X+2  X X+2
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  2  2  2  0  2  0  0  2  2  0  2  2
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  2  2  2  0  2  2  2  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  0  2  0  2  0  0  2  2  2  0  0  2  2  2  0  0  2  2  2  2  0  0  2  0  0  0  0  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  2  0  2  0  0  2  0  2  2  0  2  0  2  2  2  2  2  0  2  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+181x^44+8x^45+352x^46+76x^47+630x^48+188x^49+850x^50+476x^51+1139x^52+572x^53+1034x^54+420x^55+851x^56+244x^57+550x^58+52x^59+322x^60+12x^61+142x^62+61x^64+16x^66+13x^68+1x^72+1x^76

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 4.61 seconds.