The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 2 1 1 1 X X 1 1 1 1 1 X 1 1 1 0 1 2 X 1 0 2 1 X 1 1
0 X 0 0 0 0 0 2 2 X X+2 X X X X+2 X 0 X+2 2 X 2 X 0 2 X X 2 2 X+2 2 X+2 X 2 X+2 2 X+2 2 X 2 2 X+2 X+2 2 0 X 0 X 0 X X X 2 2
0 0 X 0 0 2 X+2 X X X X X X+2 0 0 0 2 2 X+2 X 2 0 0 X X+2 X 2 0 0 X+2 2 X 0 X+2 0 2 X+2 2 X+2 2 0 2 0 X X X X+2 X X X 0 X X+2
0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 0 X X 2 X 2 X+2 0 X+2 0 2 0 X X 0 X X+2 X+2 X X X+2 X+2 2 X X X+2 2 X+2 X 0 0 X 2 0 2 X 2 2 X+2 2 X+2
0 0 0 0 X X 2 X+2 X X+2 2 2 X 2 X+2 X X 2 2 X+2 0 X+2 0 0 0 0 X X 2 X+2 X+2 X 0 X 2 X 2 0 X X 0 0 X X+2 0 X+2 X+2 X 2 0 X+2 2 X
generates a code of length 53 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 46.
Homogenous weight enumerator: w(x)=1x^0+29x^46+74x^47+121x^48+152x^49+173x^50+236x^51+211x^52+184x^53+225x^54+180x^55+128x^56+94x^57+56x^58+52x^59+41x^60+28x^61+24x^62+18x^63+8x^64+6x^65+4x^66+2x^68+1x^82
The gray image is a code over GF(2) with n=212, k=11 and d=92.
This code was found by Heurico 1.16 in 0.279 seconds.