The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  1 X+2  1  X  1  X  1  1  X  1  1  2  1  1  1  1  2  1  X X+2  1  1  1  1 X+2  1  1  1  1  2  1  1  1  X  1  2  0 X+2  1  1  1  2  2  2  1  2  1  1  2  0  1  0  1  1
 0  1  1  0  1  1  2 X+1  1  0  1  3 X+3  0  1 X+1  1  0  1 X+3  X  1  2 X+1  1 X+2 X+1 X+1 X+1  1  2  1  1  2  1 X+2 X+1  1  0 X+3 X+1  3  1  2  2 X+2  1 X+1  1  1  1 X+1 X+1  X  1  X  1  X  1 X+3  1  1  1  1  2  2 X+3
 0  0  X  0  0  0  0  0  0  0  0  0  2  X X+2  X  X  X X+2 X+2 X+2  X X+2  X X+2  2  X  X X+2  2  0  2  0  0  X  2  2  X X+2  2  2  2  2 X+2  X  0 X+2 X+2  2 X+2  0  0  2 X+2  2 X+2 X+2  0 X+2  0  X  0  2  X  0  2  0
 0  0  0  X  0  0  0  0  X X+2 X+2  X X+2 X+2 X+2  0  2 X+2 X+2  X  2  0  0  X  X  X  2  X X+2 X+2  2  2  2 X+2  0  2 X+2 X+2  X  2  X  X  X  0 X+2  X  0 X+2  X  0  2  X  2  2  X X+2  0 X+2 X+2  X  2  2  X  X  2  0  2
 0  0  0  0  X  0  2 X+2  0  2  0 X+2 X+2  X  X  2  X X+2  X  0  X  X  X  0 X+2  2  X X+2 X+2 X+2 X+2 X+2  X  X X+2 X+2  0  0  2  X  0  X X+2 X+2  2  X  2  2  0 X+2 X+2  X  2  2 X+2  X  0  0  0 X+2 X+2  2  2 X+2  X  X  0
 0  0  0  0  0  X X+2 X+2 X+2 X+2  2  2  X X+2 X+2  X X+2  0  0 X+2 X+2  2  0  2  2  X  0  2 X+2  X  2  2  X  0  X  X  X X+2  0 X+2  0  X X+2  0 X+2 X+2  0  2  2  0 X+2  0  0 X+2  0  2 X+2  0  2  0  0  X X+2  X  X  2 X+2

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+100x^57+140x^58+270x^59+424x^60+562x^61+753x^62+964x^63+1270x^64+1422x^65+1579x^66+1654x^67+1471x^68+1346x^69+1311x^70+990x^71+715x^72+486x^73+311x^74+240x^75+128x^76+100x^77+44x^78+38x^79+18x^80+16x^81+22x^82+4x^83+4x^84+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 18.3 seconds.