The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+318x^60+220x^61+806x^62+264x^63+959x^64+412x^65+1166x^66+324x^67+987x^68+360x^69+834x^70+256x^71+618x^72+140x^73+276x^74+52x^75+106x^76+20x^77+46x^78+14x^80+6x^82+5x^84+2x^86

The gray image is a code over GF(2) with n=268, k=13 and d=120.
This code was found by Heurico 1.16 in 39.6 seconds.