The generator matrix

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

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+103x^62+124x^63+278x^64+316x^65+398x^66+704x^67+356x^68+736x^69+310x^70+308x^71+208x^72+100x^73+70x^74+16x^75+34x^76+12x^78+13x^80+2x^82+3x^84+1x^86+2x^88+1x^108

The gray image is a code over GF(2) with n=544, k=12 and d=248.
This code was found by Heurico 1.16 in 0.75 seconds.