The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+218x^58+572x^59+1016x^60+1328x^61+1737x^62+2036x^63+2591x^64+2626x^65+2863x^66+2802x^67+3120x^68+2768x^69+2415x^70+1924x^71+1721x^72+1166x^73+828x^74+458x^75+300x^76+150x^77+66x^78+28x^79+17x^80+8x^81+1x^82+4x^83+2x^84+2x^85

The gray image is a code over GF(2) with n=268, k=15 and d=116.
This code was found by Heurico 1.13 in 16.4 seconds.