The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  0  1  1 X+2  1  1  0  1  1  1 X+2  1  1  1  0  1 X+2  1  1 X+2  1  0  1  0  2  1  1  1 X+2  1  1  0  1  1  1  1  1  1  0  2  0
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  1  0  3  1 X+2 X+1  1 X+1  0  3  1  2 X+2 X+1  1 X+2  1  3  0  1  3  1 X+1  1  1 X+1  3  3  1 X+3 X+1  1  1  0 X+2 X+1 X+2  3  1  1  X
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  0  2  2  0  2  2  0  2  2  0  0  2  2  2  2  0  2  0  0  0  2  2  0  2  2  0  0  2  2  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  2  2  0  2  0  2  2  2  2  0  2  2  0  2  2  0  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  2  0  0  0  2  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  2  2  2  0  0  0  0  2  2  0  0  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  0  2  2  0  2  0  0  2  2  0  2  0  2  0  2  2  0  2  2  2  0  0  2  0  0  0  2  0  0  2  0  2  0  0  2  2  2
 0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  0  2  2  2  2  0  0  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  0  0  0  2  0  2  0  2  0  0
 0  0  0  0  0  0  0  2  0  2  0  0  0  0  0  0  2  2  0  0  2  2  0  2  0  2  2  0  2  0  2  0  2  0  2  2  2  2  2  2  0  0  0  2  2  0  2  2  0  2  2  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  0  2  0  0  2  0  0  2  2  2  0  0  2  0  0  0  2  2  0  0  2  0  0  2  2  0  0  0  2  0  0  2  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+110x^44+36x^45+122x^46+208x^47+418x^48+448x^49+556x^50+880x^51+879x^52+968x^53+784x^54+816x^55+658x^56+544x^57+308x^58+144x^59+173x^60+52x^61+22x^62+41x^64+21x^68+2x^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 3.18 seconds.