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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 2 1 1 1 1 1 2 1 2 2
0 2X+2 0 2X+2 0 2X+2 0 2 2X 2X+2 2X+2 0 0 2X+2 2X 2 0 2X 2X+2 2 2X+2 2 0 2X 0 2X 2X+2 2 0 2X 2X 2X+2 2X+2 2 2 0 0 2X 2X 0 2X 2X+2 2 2X 2 2 2X+2 0 2X 2X 2 0 2X
0 0 2X 0 0 0 0 0 2X 0 0 0 2X 0 2X 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 0 2X 0 2X 0 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 2X 0 2X 2X 0 2X 2X 0 0
0 0 0 2X 0 0 0 2X 0 0 0 0 0 2X 0 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X
0 0 0 0 2X 0 0 0 0 0 0 2X 2X 0 2X 0 0 2X 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 2X 2X 2X 2X 2X 0 0 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 0 0
0 0 0 0 0 2X 0 2X 0 0 2X 0 0 2X 0 0 2X 2X 0 2X 0 2X 0 0 2X 2X 2X 0 0 2X 0 0 0 2X 2X 2X 0 2X 2X 2X 0 0 2X 0 0 2X 2X 2X 2X 0 0 2X 0
0 0 0 0 0 0 2X 0 2X 2X 2X 2X 0 2X 2X 2X 2X 2X 0 2X 0 2X 2X 2X 2X 2X 0 2X 2X 2X 2X 2X 0 0 2X 2X 0 2X 0 0 0 0 0 0 2X 2X 0 0 0 0 2X 2X 0
generates a code of length 53 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+132x^48+32x^49+64x^50+128x^51+86x^52+1216x^53+64x^54+128x^55+88x^56+32x^57+56x^60+18x^64+2x^68+1x^96
The gray image is a code over GF(2) with n=424, k=11 and d=192.
This code was found by Heurico 1.16 in 0.219 seconds.