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  0  2  0  0  X  1  0  1  1  X  0  X  X  2  X  X  1  1  2  1  X  1
 0  X  0  0  0  0  0  0  0 X+2  X  X  X  X  2  2  0  X  2 X+2  X  0  2  2  X  0  X X+2  2 X+2  0  2  X  X  2  2  0  0  X  0  X  X X+2 X+2  X  0 X+2  2  X  X X+2 X+2  2
 0  0  X  0  0  0  X X+2  X  2  X X+2  0  0  X X+2 X+2 X+2  0  2  X X+2 X+2 X+2  X  2 X+2  X X+2  0  0  X X+2 X+2  2  0  X  X  2  2  X  0  X X+2  0  X  0 X+2  X X+2  X  2 X+2
 0  0  0  X  0  X  X  X  0 X+2  2  X X+2  0  X X+2  0  0 X+2  X  2  X  0  2  2  0  X  X  0  X  0  2  0  2  X  0 X+2  X  X  2 X+2 X+2  0 X+2  0  2  2  2  0 X+2  X  2  0
 0  0  0  0  X  X  0  X X+2  X  0  X  2 X+2 X+2  0  X X+2  2  2  0 X+2  X  0  0  X X+2  0  2 X+2  2  0  0  X  0  X X+2 X+2  2  0  2 X+2 X+2 X+2 X+2  2  X  X X+2  0 X+2  2 X+2
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  2  2  2  0  0  2  2  2  2  2  0  2  2  2  2  2  0  2  2  2  0  2  2  0  0  0  0  0  2
 0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  2  2  0  2  0  2  2  0  2  0  2  2  0  2  0  2  0  0  2  0  0  2  0  0  0  0  2  0  0  2  2  2  0  0  2  2  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+169x^44+405x^46+52x^47+624x^48+232x^49+806x^50+452x^51+1070x^52+600x^53+1118x^54+444x^55+884x^56+184x^57+506x^58+76x^59+314x^60+8x^61+147x^62+67x^64+24x^66+6x^68+2x^70+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 4.53 seconds.