The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X 1 1 1
0 2X 0 0 0 0 0 0 0 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 0 0 0
0 0 2X 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 2X 2X 0 0 0 0 0
0 0 0 2X 0 0 0 0 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 0 0 0 0
0 0 0 0 2X 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 0
0 0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 2X 0 0 0 0
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 0 0 2X 0 0 0
0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 0 0 0
generates a code of length 23 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+78x^16+32x^19+52x^22+1728x^23+48x^24+32x^27+72x^30+1x^32+4x^38
The gray image is a code over GF(2) with n=184, k=11 and d=64.
This code was found by Heurico 1.16 in 0.031 seconds.