The generator matrix

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

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+203x^28+280x^29+482x^30+648x^31+928x^32+1120x^33+974x^34+1136x^35+800x^36+632x^37+494x^38+264x^39+156x^40+16x^41+34x^42+21x^44+3x^48

The gray image is a code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.16 in 1.31 seconds.