The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  1 X+2  1  X  1  1  X  X  1  1  1  1  2  2  1  X  1  2  1  1  2  1  1 X+2  1  1  2  1  1  1  1  X  2  0  0  1  1  1  1  1
 0  1  1  0  1  1  2 X+1  1  0  1  3 X+3  0  1  1  1  2  2  1  1  2  3 X+1  3  1  1  0  1 X+2  1 X+1  0  1 X+1  2  1  1  3  1 X+2 X+3  0  X  X  1  1  1 X+3 X+2  2  X X+1
 0  0  X  0  0  0  0  0  0  0  0  0  2  X X+2 X+2 X+2 X+2 X+2  X  X  X  X X+2  2  2  2  X  2  0 X+2  X  0  X  2 X+2  2  2  X X+2  X  0  2  2 X+2  X  0  X  2  2  X  2  2
 0  0  0  X  0  0  0  0  X X+2 X+2  X X+2 X+2 X+2 X+2  0 X+2  2 X+2  2  0  0 X+2  2  X  0  0  2  2  X  0 X+2  2 X+2  X X+2  2  0 X+2 X+2  2 X+2  X X+2  X  2  2 X+2  0 X+2  X X+2
 0  0  0  0  X  0  2 X+2  0  2  0 X+2  X  X  X  2  X X+2  X  X  X X+2  2  0  0 X+2  X  2 X+2  X  2  X  X  X  X  0  X  0  X X+2  0  0 X+2  2  0  2  X  X  2  X X+2 X+2 X+2
 0  0  0  0  0  X X+2 X+2 X+2 X+2  2  2  X X+2 X+2  2  2  0 X+2  0  X  0 X+2 X+2  2  X  X  X  0 X+2  2  X X+2  X  2 X+2  0  0  2  0  2  2  X  0  0  X  0  0 X+2 X+2 X+2  X  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+156x^44+32x^45+478x^46+336x^47+780x^48+1048x^49+1204x^50+1684x^51+1512x^52+1996x^53+1544x^54+1720x^55+1183x^56+976x^57+688x^58+356x^59+386x^60+44x^61+162x^62+75x^64+20x^66+2x^68+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 11.5 seconds.