The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+110x^60+100x^62+296x^64+220x^66+630x^68+220x^70+259x^72+100x^74+81x^76+19x^80+10x^84+1x^88+1x^108

The gray image is a code over GF(2) with n=272, k=11 and d=120.
This code was found by Heurico 1.16 in 0.564 seconds.