The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  2  1  1  1  X  1  X  1  1  1  1  2  1  0  1  1 X+2  1  1  2  1  1  1 X+2  1  1  0  0  1  1  X  1  2  1  1  1  1  1  1  1  0  X  1 X+2  1  1  1  1 X+2  1  1  1  1  0  1
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  1  0 X+1 X+2  1  3  1  2 X+1  3  X  1  2  1 X+3 X+2  1 X+2 X+1  1 X+1  2  1  1 X+2 X+3  1  1  0  0  1 X+1  1  2 X+3 X+1  1 X+2 X+3  2  1  2  2  1  0  2 X+1 X+3  1  2 X+2  3  2  0  1
 0  0  X  0  0  0  0  0  0  2  2 X+2  X  X  2  X X+2  X X+2  X  X  0 X+2 X+2  2  0  X  X  0  2  2 X+2  2  0  2  X  0  X  2  0  2  X  0 X+2  2  X X+2  X X+2  0  2  X  2  X X+2  0  X  2  0  X  X X+2 X+2  0 X+2  X X+2
 0  0  0  X  0  0  X  2  X  2 X+2  2 X+2  2  X  0  X X+2  0  X  X X+2 X+2  0  X  0 X+2  X  X  2  0  2 X+2  X  X  0  X  X  X  0  2  2  2  2 X+2  0  0  X  X  X X+2  2  2 X+2  0  2 X+2  0  2  2 X+2  0 X+2  0  2  2  X
 0  0  0  0  X  0  0 X+2  2  0  2  2 X+2  X X+2  X  X  2  X  X  0  X  X X+2  0  2 X+2  0  X  X  0  0  2  X  2  2  X  X  X X+2 X+2  X X+2  0  X  2 X+2  X  X  0  X  X X+2  0  0  2 X+2  2  0  0  0 X+2  X  0  2  X X+2
 0  0  0  0  0  2  0  0  2  0  2  0  2  0  0  0  2  0  2  0  2  2  2  0  2  0  0  0  2  2  0  0  2  0  0  2  0  2  0  2  0  2  0  2  2  2  0  2  0  2  0  2  2  2  0  2  0  2  0  2  2  0  0  0  2  2  2
 0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  2  0  2  2  2  2  0  2  2  2  2  2  0  0  0  2  0  0  0  2  2  2  0  2  2  2  2  2  2  2  0  0  2  0  0  2  0  0  2  2  2  0  0  2  0  0  2  2  2  2  0  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+56x^57+175x^58+306x^59+407x^60+544x^61+725x^62+974x^63+1333x^64+1458x^65+1519x^66+1616x^67+1555x^68+1424x^69+1117x^70+934x^71+776x^72+500x^73+364x^74+228x^75+129x^76+96x^77+54x^78+36x^79+21x^80+18x^81+10x^82+2x^83+4x^86+1x^88+1x^92

The gray image is a code over GF(2) with n=268, k=14 and d=114.
This code was found by Heurico 1.16 in 22.2 seconds.