The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+172x^26+48x^27+480x^28+236x^29+1076x^30+924x^31+2082x^32+1868x^33+2619x^34+1852x^35+2096x^36+932x^37+1094x^38+244x^39+436x^40+36x^41+152x^42+4x^43+23x^44+6x^46+1x^48+1x^50+1x^60

The gray image is a code over GF(2) with n=136, k=14 and d=52.
This code was found by Heurico 1.16 in 9.07 seconds.