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 X 2 1 1 1 1 1 X 1 1 2 1 1 1 X 1 X 1 0 1 1 1 X 1 X 1 1 X 1 1 0 1 1 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 X 2 X+2 X+2 2 X+2 2 X+2 X 0 X 2 X X 0 2 2 0 X+2 X+2 X 0 0 0 X 0 2 0 2 X 2 X X+2 X X+2 X+2 X+2 X+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+2 2 2 0 0 0 X+2 X+2 X X+2 0 X 2 X+2 2 X X X+2 X+2 X X X X 2 X 0 2 2 0 0 0 2 X+2 X 0 X+2 0 X
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 X 2 X 0 X X X 0 X 2 X 2 X+2 2 0 X+2 X X 0 2 X 2 2 0 X+2 2 2 X 0 X+2 2 0 X 0 0 X X+2 X
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 X+2 X+2 X+2 2 X 0 X 0 2 X 2 2 0 0 2 0 2 X+2 X+2 X X+2 0 X+2 0 0 X+2 2 X 0 X X+2 0 X 0 X+2 0 0 0
generates a code of length 61 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+80x^54+4x^55+185x^56+68x^57+272x^58+88x^59+311x^60+188x^61+262x^62+116x^63+170x^64+28x^65+102x^66+16x^67+66x^68+4x^69+42x^70+32x^72+10x^74+2x^76+1x^100
The gray image is a code over GF(2) with n=244, k=11 and d=108.
This code was found by Heurico 1.16 in 0.359 seconds.