The generator matrix

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

generates a code of length 68 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+460x^62+1308x^63+2054x^64+3036x^65+3653x^66+3942x^67+4452x^68+3998x^69+3341x^70+2824x^71+1658x^72+1008x^73+617x^74+198x^75+92x^76+56x^77+39x^78+15x^80+12x^81+2x^82+2x^85

The gray image is a code over GF(2) with n=544, k=15 and d=248.
This code was found by Heurico 1.16 in 10.4 seconds.