The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X  X  2  0  1  1  1  1  2  1  1  1  1  2  1  1  1  1  1 X+2  2  1  X  1  1  1  X  X  2  2  2  1  X  2  1  1  1  1  1
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1  1  1  X  1  X  1  X  3  0 X+1  1  2 X+2  1  1  X  0  X  3 X+1  3  1  1  0  0 X+2 X+2  1  1  1  1  1  1  0  0  1 X+3  0  1  1  0
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  1  0  X X+1  1  2  1 X+1  X  0 X+1 X+3  1  1  0  0  X  1 X+3  1 X+1  3  X  0  0  X  1 X+2 X+3 X+1  1 X+3 X+2  2  0 X+3  1 X+1  2 X+2  1  1  0
 0  0  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  0  0  2  0  0  0  2  2  0  2  2  0  0  0  0  0  0  2  2  2  2  2  2
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  0  2  0  0  2  2  2  2  2  2  0  2  2  2  0  2  2  0  2  2  2  2  0  0  2  2  0  0  0  2  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  2  2  2  0  2  0  0  2  2  0  2  2  2  0  0  2  0  0  0  0  2  0  0  2  2  2  2  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  2  2  0  0  2  0  2  2  2  0  2  2  2  2  0  2  0  0  2  2  2  2  0  2  2  0  0  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  2  2  0  2  0  0  2  2  0  0  0  0  2  0  2  2  0  2  2  2  2  0  0  2  2  2  0  0  0  2  0  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+44x^44+142x^45+267x^46+656x^47+673x^48+1124x^49+1172x^50+1740x^51+1457x^52+1986x^53+1486x^54+1634x^55+1125x^56+1182x^57+582x^58+538x^59+252x^60+168x^61+69x^62+38x^63+24x^64+6x^65+6x^66+2x^67+7x^68+2x^70+1x^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 9.09 seconds.