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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+178x^56+530x^58+28x^59+799x^60+112x^61+1096x^62+472x^63+1549x^64+892x^65+1942x^66+1116x^67+2173x^68+892x^69+1558x^70+404x^71+1068x^72+148x^73+660x^74+24x^75+397x^76+4x^77+202x^78+4x^79+100x^80+28x^82+6x^84+1x^100

The gray image is a code over GF(2) with n=268, k=14 and d=112.
This code was found by Heurico 1.16 in 21.3 seconds.