The generator matrix

 1  0  0  0  1  1  1  1  2  1  X  1 X+2  1  2  X  X  2  1  0  1  2  1  1  0  1  X  1  2 X+2 X+2  1 X+2  1 X+2  X  1  1  1  1 X+2  2  1  1  1  2  0  1  1  X  1  1  1
 0  1  0  0  0  2  1  3  1 X+2  0 X+1  1  1  1  1  1  2  0  0 X+2 X+2  3 X+3  1 X+2  1  2  1  2  0  3  1 X+2  2  1  0 X+3  1  X  1  1  3 X+3  X  1 X+2  X  0  2 X+3  1  2
 0  0  1  0  0  3  1  2  3  1  1  3  X X+2  1  X  2  1 X+3  1  1  0 X+3  X  2 X+3 X+2 X+2  3  2  1 X+2  1 X+2  1  0  X X+3  0 X+2 X+3 X+1  X X+3 X+3 X+2  1 X+1 X+1  1 X+2 X+3  0
 0  0  0  1  1  1  2  3  3  0 X+3  3 X+3 X+2  X  1  0  X  3  1 X+2  1 X+3 X+2  X  1  3  3  3  1 X+3  3  2  2  0  X  1  0  2 X+1  0 X+2  X  2 X+2  0  0  X  X X+2  1  X  0
 0  0  0  0  X  0  0  0  0 X+2  X  X  X X+2 X+2  X  2  2  2 X+2  X  2  X  2  X X+2  2  0  X  X  0 X+2 X+2  X X+2  2  X  2 X+2  2  0  0  0 X+2  X X+2 X+2  0  2  X X+2  0  X

generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+86x^45+327x^46+700x^47+754x^48+1142x^49+1274x^50+1566x^51+1517x^52+1758x^53+1481x^54+1690x^55+1282x^56+980x^57+730x^58+558x^59+209x^60+168x^61+84x^62+42x^63+13x^64+10x^65+6x^66+4x^67+2x^70

The gray image is a code over GF(2) with n=212, k=14 and d=90.
This code was found by Heurico 1.13 in 3.38 seconds.