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

generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+8x^43+248x^44+12x^45+300x^46+112x^47+606x^48+256x^49+790x^50+368x^51+1175x^52+504x^53+1056x^54+448x^55+897x^56+224x^57+532x^58+72x^59+315x^60+28x^61+132x^62+16x^63+60x^64+6x^66+21x^68+3x^72+1x^76+1x^80

The gray image is a code over GF(2) with n=212, k=13 and d=86.
This code was found by Heurico 1.16 in 27 seconds.