The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 2 X 1 1 1 X 2 2 0 X
0 X 0 0 0 0 0 2 2 X X+2 X 2 X+2 X X 0 X+2 0 2 X+2 X+2 X X 2 X X 0 0
0 0 X 0 0 2 X+2 X X X X X X+2 2 X 2 0 2 X 2 X 2 X+2 0 0 0 0 0 0
0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 X X+2 X+2 2 2 2 X X 0 X+2 X X X 2 X+2 2 0
0 0 0 0 X X 2 X+2 X X+2 2 2 0 X X X 0 0 0 X X 2 X X 2 X+2 0 X 0
generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+217x^24+68x^25+88x^26+244x^27+274x^28+392x^29+84x^30+264x^31+203x^32+52x^33+80x^34+4x^35+70x^36+4x^38+3x^40
The gray image is a code over GF(2) with n=116, k=11 and d=48.
This code was found by Heurico 1.16 in 0.121 seconds.