The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  0  1 X+2 X+2  1  1  1  0  X  1  1  X  2  1  1  0  1  2  0  X  1  1  0  X X+2  X  1  2  0 X+2  1  1 X+2  0  1  1  1  X  1  0  1  1  0  2 X+2  1  0  1  1  1  1 X+2  1  2  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  3  1  1  3  2  2  2  2 X+1 X+1  1  1  X X+2  1 X+1  0  1 X+2  3 X+1  0  1  1  1 X+1  X  1  1  3  1  1  1  2  X X+3  X  0  1  3  3 X+2 X+2  0 X+2  1 X+1  3 X+2  X  1  2  1  3  X
 0  0  1  0  0  0  1  1  1  3  1  2  X  1 X+1  0 X+1  3  1  1  1 X+1 X+1  3  2  X X+2  0  2 X+2  2  X  X  1  0  1  X  3 X+2 X+1 X+2 X+1  0  1  1  2  2  0  1 X+1  0 X+1 X+1  1  1  1  3  0  X X+3  3  3 X+1  0 X+2 X+2 X+2
 0  0  0  1  0  1  1  0  3  2 X+1 X+3 X+2  3  X X+3  1 X+2  3  0 X+3 X+2  1  2  X X+1  3  0  1  2  0  0  1  X  X X+3  1  3  1  X  X  3 X+3 X+3  0 X+1  0 X+1 X+1  1 X+1 X+3  2 X+2 X+1  1 X+2  1 X+2 X+1  2  X X+1 X+2 X+3 X+2  3
 0  0  0  0  1  1  2  3  1  0 X+1 X+3 X+1  0  1  2 X+3  X X+2 X+1  2  3 X+1  X X+1  0  X X+3 X+3 X+1  1 X+2 X+1  0 X+2  X  1  X  0  3 X+1 X+3  X  3  0  2  3  3 X+2  0  2  0  1  X X+1 X+3  2  0  1  X  1  0  2 X+2 X+1  X  0
 0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  2  0  0  2  0  2  2  0  2  0  0  2  2  2  2  0  0  2  2  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  0  2  0  2  2  2  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+262x^57+631x^58+1284x^59+1683x^60+2596x^61+2771x^62+4316x^63+4448x^64+5490x^65+5755x^66+6600x^67+5909x^68+6102x^69+4613x^70+4260x^71+2859x^72+2450x^73+1296x^74+1056x^75+538x^76+288x^77+156x^78+80x^79+48x^80+22x^81+10x^82+4x^83+2x^84+6x^85

The gray image is a code over GF(2) with n=268, k=16 and d=114.
This code was found by Heurico 1.13 in 62.7 seconds.