The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 X 1 X 2 X X 0 1
0 X 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 X+2 X X X+2 2 X X X X 2 2 X X+2 X 2 X+2 X 0
0 0 X 0 0 0 0 0 0 0 X X+2 X X+2 X+2 X X+2 X X X+2 2 0 0 X 2 2 X+2 2 0 X 2 X X+2 0 0
0 0 0 X 0 0 0 X X+2 X X X 0 X+2 X 0 0 0 X 2 X+2 X X+2 X+2 2 0 X+2 X 2 X 2 X 0 2 X
0 0 0 0 X 0 X X X 2 0 0 2 X+2 X X+2 X 0 X+2 X+2 X X X 2 2 2 0 0 X 2 0 X X 0 0
0 0 0 0 0 X X 2 X+2 X+2 0 X X X 2 0 X X 2 2 0 X+2 X+2 X X 0 0 X+2 0 0 X+2 2 2 2 X
0 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 0 2 2 0 0 0 2 0 2 0 0 2 2 2 0 2 0 2
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+144x^26+543x^28+8x^29+854x^30+176x^31+1665x^32+1016x^33+2867x^34+1696x^35+3044x^36+1016x^37+1690x^38+176x^39+859x^40+8x^41+428x^42+149x^44+32x^46+10x^48+1x^50+1x^56
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 8.61 seconds.