The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+36x^46+102x^47+246x^48+334x^49+476x^50+692x^51+994x^52+1260x^53+1497x^54+1746x^55+1662x^56+1758x^57+1614x^58+1192x^59+937x^60+684x^61+432x^62+254x^63+208x^64+106x^65+64x^66+44x^67+13x^68+16x^69+7x^70+2x^71+3x^72+2x^73+2x^74

The gray image is a code over GF(2) with n=224, k=14 and d=92.
This code was found by Heurico 1.16 in 12.4 seconds.