The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  1  1  0  1  0  X  1  1  1  1  1
 0  X  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  0 X+2  2  X  0  0  0  2 X+2  X X+2  2  2  X X+2  X X+2 X+2  0  2  0  0
 0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  0  0  0  2  2  2  0  0  2  0  0  2  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  2  2  2  2  0  2  2  2  2  2  2  2  0  2  2  2  2  2
 0  0  0  0  2  0  0  0  0  0  2  0  2  0  2  0  2  0  2  0  0  2  2  0  0  2  2  2  0  2  2  0  0  2
 0  0  0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  2  2  2  0  2  0  0  0  0  2  2  2  0  0  0  2  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  0  0  2  0  0  0  2  2  0  2  2  0  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  0  0  2  2  0  0  0  2  0  2  0  2  2  2  2  0  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+146x^28+64x^30+128x^31+248x^32+384x^33+128x^34+384x^35+236x^36+128x^37+64x^38+115x^40+18x^44+3x^48+1x^56

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 86.1 seconds.