The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+320x^62+667x^64+908x^66+727x^68+610x^70+359x^72+258x^74+144x^76+70x^78+20x^80+10x^82+1x^84+1x^88

The gray image is a code over GF(2) with n=272, k=12 and d=124.
This code was found by Heurico 1.16 in 6.29 seconds.