The generator matrix

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

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+234x^62+224x^63+407x^64+280x^65+550x^66+372x^67+475x^68+236x^69+308x^70+180x^71+267x^72+128x^73+132x^74+76x^75+113x^76+28x^77+42x^78+12x^79+17x^80+14x^82

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 1.14 seconds.