The generator matrix

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

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+45x^26+62x^27+223x^28+338x^29+561x^30+842x^31+1235x^32+1696x^33+2022x^34+2332x^35+2033x^36+1692x^37+1283x^38+852x^39+547x^40+288x^41+166x^42+70x^43+52x^44+18x^45+16x^46+2x^47+5x^48+3x^50

The gray image is a code over GF(2) with n=140, k=14 and d=52.
This code was found by Heurico 1.16 in 5.77 seconds.