The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+291x^60+524x^61+676x^62+936x^63+1311x^64+1088x^65+1424x^66+1296x^67+1505x^68+1384x^69+1344x^70+1052x^71+1180x^72+880x^73+554x^74+376x^75+269x^76+124x^77+90x^78+20x^79+44x^80+6x^82+7x^84+2x^86

The gray image is a code over GF(2) with n=272, k=14 and d=120.
This code was found by Heurico 1.13 in 5.81 seconds.