The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  2  1 X+2  1  1  1  0  1  1  1  1  X  1  X  1  0  1  1  0  X  X  1  1  1  0  1  1  X  1  1  1  1  0  1  X  1  0  1  0  2  2
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  1  0  1  3 X+1  2  1 X+2 X+1 X+2  3  1 X+1  1  X  1  1  0  1  1  1 X+1  X  1  1  2  2  1  1  3  X  2  1  2  0  2  1  2  0  2  1
 0  0  X  0  0  0  0  0  0  2  2 X+2  X  X  X  2 X+2  X  X X+2  2  X  X X+2  2  2 X+2 X+2 X+2 X+2  X  2  X  2  2 X+2 X+2  0  X  0  2 X+2  2  2 X+2  X  2  X  2  X  0  X  X
 0  0  0  X  0  0  X  2  X  2 X+2  2 X+2  2  0 X+2  X  X  0  0 X+2  X  X  X X+2 X+2 X+2  2  X X+2 X+2 X+2  2  2  0 X+2  0 X+2 X+2 X+2  2  X X+2  2  X  X  X  0  2  X  2  X  2
 0  0  0  0  X  0  0 X+2  2  0  2  2 X+2  X  X  X  0 X+2 X+2 X+2  X  X  0  X  X  2 X+2  X  X  2  2 X+2  2  2  X X+2  2 X+2  2  X  X X+2  2 X+2  X X+2  2  X X+2  X  X  0  2
 0  0  0  0  0  2  0  0  2  0  2  0  2  0  2  0  0  0  2  2  2  2  2  2  2  0  2  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  2  2  0  0  2  0  0  0  0  2
 0  0  0  0  0  0  2  2  0  2  2  2  2  0  2  2  0  0  0  0  2  0  2  0  0  0  2  0  2  0  0  2  0  2  2  2  0  2  0  2  2  0  2  0  2  2  2  0  0  0  2  0  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+72x^45+448x^46+376x^47+849x^48+968x^49+1146x^50+1648x^51+1500x^52+1984x^53+1464x^54+1768x^55+1232x^56+1000x^57+724x^58+288x^59+376x^60+72x^61+168x^62+16x^63+68x^64+18x^66+8x^68+2x^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 11.6 seconds.