The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 X 2X+2 1 1 1 X 2X X 2 X X X X 1 1 1 1 X 1
0 X 2X+2 X+2 2X 3X+2 2 3X 0 X+2 2X+2 3X X+2 X 2X 3X X 3X+2 2 X 3X+2 X X X 0 2X+2 2X 2 0 2X+2 2X 2 X+2 0
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+18x^33+85x^34+18x^35+2x^37+2x^39+1x^42+1x^44
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 0.015 seconds.