The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1  X  1  1  1  1  X  1  1  X  1  1  2  1  0  X  1  2  1  1  2  1  1  0  0  1  2  X  X  1  X  X  1
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2 X+2 X+2  2  0  0 X+2  2 X+2  0  2  X  X  2  X  0  X X+2  2  X  0 X+2  0 X+2  2 X+2  X  0 X+2 X+2  2  2  X  0  X  X X+2  X  2 X+2  X  X  X  2  0  2  2  0  0 X+2 X+2  2  2
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  2  0 X+2 X+2  2 X+2  2  0  2  X  2  X  X  X  0  2  0  X  X  2  2 X+2 X+2 X+2  X  2  0  X  X  2  0 X+2  2 X+2  0  0  X  2  X  0  X  X  X  X  2  X X+2  X  2  2 X+2  0
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0 X+2  0  X  2  X  X  0  0  X  2 X+2 X+2  X  X X+2 X+2 X+2  0  0  2  0  2  2  X  0  X X+2  2 X+2  X X+2  X  2 X+2 X+2  X  0 X+2  2 X+2  0  0  0  0  0  2 X+2 X+2  2  X X+2  X
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  2  2  0  0  0  0  0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  2  0
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  0  2  2  0  2  0  0  2  0  0  2  0  2  0  0  2  2  2  2  2  0  0  2  0  0  0  0  2  0  2  2  0  2  0  2  0  0  2  0  2  0  2  0  0  2
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  0  2  0  2  2  2  2  2  2  0  0  0  0  0  2  2  0  2  2  2  0  2  2  2  0  2  0  0  2  0  0  2  2  2  2  2  2  2  0  0  0  2  0  0  2  0  2  2  0  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+62x^60+82x^61+132x^62+188x^63+190x^64+250x^65+320x^66+360x^67+355x^68+382x^69+357x^70+316x^71+283x^72+218x^73+133x^74+112x^75+97x^76+80x^77+57x^78+32x^79+34x^80+12x^81+23x^82+16x^83+2x^84+1x^86+1x^102

The gray image is a code over GF(2) with n=276, k=12 and d=120.
This code was found by Heurico 1.16 in 1.46 seconds.