The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+100x^60+210x^61+539x^62+670x^63+1013x^64+916x^65+1375x^66+1168x^67+1668x^68+1344x^69+1577x^70+1208x^71+1358x^72+860x^73+912x^74+452x^75+453x^76+210x^77+153x^78+78x^79+41x^80+40x^81+13x^82+4x^83+3x^84+4x^85+7x^86+4x^87+3x^88

The gray image is a code over GF(2) with n=276, k=14 and d=120.
This code was found by Heurico 1.16 in 13.5 seconds.