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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+74x^57+133x^58+172x^59+214x^60+344x^61+254x^62+670x^63+237x^64+1158x^65+218x^66+1422x^67+244x^68+1084x^69+225x^70+634x^71+190x^72+302x^73+127x^74+146x^75+100x^76+100x^77+56x^78+24x^79+36x^80+10x^81+10x^82+4x^83+2x^84+1x^102

The gray image is a code over GF(2) with n=268, k=13 and d=114.
This code was found by Heurico 1.16 in 6.44 seconds.