The generator matrix

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

generates a code of length 68 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+88x^59+753x^60+2270x^61+4880x^62+8412x^63+13429x^64+21528x^65+27870x^66+34064x^67+34853x^68+34604x^69+28497x^70+21740x^71+13612x^72+8126x^73+4051x^74+1900x^75+920x^76+330x^77+129x^78+48x^79+8x^80+6x^81+8x^82+4x^83+8x^84+4x^86+1x^90

The gray image is a code over GF(2) with n=544, k=18 and d=236.
This code was found by Heurico 1.16 in 607 seconds.