The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0 X+2  1  1  1  1  0 X+2  1  1  1  1  0 X+2  1  1  1  1 X+2  0  X  1 X+2  1  1  1  1  0  1  1  1  2  1  2  1  X  2  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1  1 X+2  3  3 X+2  1  1 X+1  0  3 X+1  1  1  3  0 X+1  0  1  1  1 X+2  1  0 X+3 X+1  2  1 X+1 X+2  3  1 X+3  1 X+1  1  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  0  2  2  2  2  2  2  0  0  2  2  0  0  2  2  0  2  0  0  2  2  0  2  0  0  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  2  0  2  2  2  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  2  2  0  0
 0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  0  2  2  2  2  2  2  0  2  2  2  2  2  2  0  2  2  2  0  0  2  2  0
 0  0  0  0  0  2  0  0  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  0  2  2  0  0  0  2  0  2  0  2  2  2  0  2  0  2  2  0  0  2  2  0  2  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  0  0  2  2  0  0  0  0  2  2  2  2  0  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0
 0  0  0  0  0  0  0  2  2  2  2  0  0  0  2  2  0  2  0  2  0  2  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  0  2  0  0  0  2  2  2  0  2  0  0  2  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+28x^44+8x^45+134x^46+96x^47+189x^48+296x^49+285x^50+368x^51+418x^52+488x^53+355x^54+448x^55+292x^56+216x^57+212x^58+112x^59+78x^60+16x^61+30x^62+10x^64+7x^66+4x^68+1x^70+4x^72

The gray image is a code over GF(2) with n=212, k=12 and d=88.
This code was found by Heurico 1.16 in 0.723 seconds.