The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 X X X X 2 0 1 X 2 0 1 1 2 2X 2 2X
0 2X+2 0 2X+2 2X 2 2X 2 0 2X+2 0 2X+2 2X 2X+2 2X+2 2X 2 2 0 2X 2 2 2X+2 2 0 2X 2X+2 2 0 2X 2 2 2 2
0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 0 2X 0 2X 0 2X 2X 2X 0 0 2X 0 0 2X 0 2X 2X 2X 0 0 2X
generates a code of length 34 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 33.
Homogenous weight enumerator: w(x)=1x^0+14x^33+102x^34+6x^36+1x^38+1x^40+2x^41+1x^46
The gray image is a code over GF(2) with n=272, k=7 and d=132.
This code was found by Heurico 1.16 in 0.047 seconds.