The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+94x^45+387x^46+1022x^47+1779x^48+2830x^49+4147x^50+5636x^51+7801x^52+9888x^53+11714x^54+12932x^55+13514x^56+13446x^57+12424x^58+10344x^59+7726x^60+5886x^61+3967x^62+2486x^63+1466x^64+698x^65+499x^66+196x^67+89x^68+52x^69+12x^70+24x^71+8x^72+2x^73+2x^74

The gray image is a code over GF(2) with n=224, k=17 and d=90.
This code was found by Heurico 1.13 in 178 seconds.