The generator matrix

 1  0  1  1  1 X^2+X  1  1  2  1  1 X^2+X+2  1 X^2+2  1  1  X  1 X^2 X+2  1  1  1  1  1  1  1  1  X  1 X^2+2  0  1 X^2+2
 0  1 X+1 X^2+X X^2+1  1  3  2  1 X^2+X+1 X^2+X+2  1 X^2  1 X^2+3 X+2  1 X+1  1  1 X^2+2 X^2+X+3  X  1  0  0 X+3 X^2 X+2 X+2  1 X^2  3  1
 0  0 X^2  0  2  0  2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2  0 X^2+2  2 X^2  0 X^2  2  0  2 X^2 X^2+2  0 X^2 X^2  2 X^2+2  2  2 X^2+2 X^2  2
 0  0  0  2  2  2  0  2  0  2  0  2  0  2  0  0  0  2  2  0  2  0  2  2  2  0  2  0  0  2  0  2  0  2

generates a code of length 34 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+234x^31+292x^32+368x^33+353x^34+340x^35+200x^36+168x^37+46x^38+34x^39+1x^40+8x^41+1x^42+2x^44

The gray image is a code over GF(2) with n=272, k=11 and d=124.
This code was found by Heurico 1.16 in 133 seconds.