The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 0 X X X 1 0 1 1 X 2 1 1 0 X X
0 X 0 0 0 0 0 2 2 X X+2 X 2 X+2 X+2 X X+2 2 X X X 0 X+2 0 X 0 2 X+2 X X+2 2 X 0 X+2
0 0 X 0 0 2 X+2 X X X X X X+2 2 X+2 2 2 0 X+2 0 2 X 0 0 X 0 X+2 0 0 2 2 X+2 X+2 X+2
0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 X X+2 0 X+2 2 2 0 2 2 0 X 2 X 2 0 X 2 X+2 2 X X+2 X+2
0 0 0 0 X X 2 X+2 X X+2 2 2 0 X X 0 X X+2 X+2 2 X X X 0 X X 0 X+2 X+2 0 0 X+2 X X+2
generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+85x^28+24x^29+248x^30+88x^31+317x^32+144x^33+310x^34+144x^35+277x^36+88x^37+172x^38+24x^39+65x^40+38x^42+22x^44+1x^48
The gray image is a code over GF(2) with n=136, k=11 and d=56.
This code was found by Heurico 1.16 in 0.14 seconds.