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  1  1  0  1  X  X  1  1  1  2  1  X  1  X  X  1  1  X  1  1  2  1  1  1  1  1  1  1  0  X  0  X  X  X  1  X  1  1
 0  X  0  0  0  0  0  0  2  X X+2 X+2  X  X  X  X  2  0  2  2  X X+2 X+2 X+2 X+2 X+2 X+2  2  0  0  2  X  0  0 X+2  X X+2 X+2  2 X+2  2  X  2 X+2  0  2  X X+2  X  2  0  X  2  0 X+2  0 X+2  X  2  2  0  0  X X+2  0  X  2 X+2  2
 0  0  X  0  0  0  X X+2 X+2  X  X  2  X  X X+2  0  2  2 X+2  X  2  0  X  2  X  2  0  X  0  X  0 X+2 X+2  2  X  X X+2  0  X X+2  2  X  X  2  2  0  0 X+2  2  0 X+2  X  2  X  X  0 X+2 X+2  0  X  X  X  2  2 X+2  0  0  X  0
 0  0  0  X  0  X  X  X  0  2  0  X X+2 X+2  2  0 X+2  2 X+2  0 X+2  2  2 X+2  X  0 X+2  2  X X+2  0 X+2 X+2  X  2  X  X  0  0  2  X X+2  2  2 X+2  X  X  X X+2 X+2  0  X  X  2  2  0  0 X+2  X  0  0  2  0 X+2  0 X+2  X  X  2
 0  0  0  0  X  X  2 X+2  X  2  X  0  X  0  X  0  2  0  X X+2 X+2  X  2  2  X X+2 X+2  2 X+2  2 X+2  0  2  2  0 X+2  2  X  2  X  X X+2  0  2  X X+2  X X+2  0 X+2  2  X  2  2 X+2  0  0  2  2  X  X  0  X  0  0 X+2  0  2 X+2
 0  0  0  0  0  2  2  2  0  0  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  2  2  2  0  0  2  2  2  0  0  2  2  2  0  2  0  0  2  0  2  2  2  2  2  2  2  2  2  0  2  2  2  2  2  2  0  2  2  0  0  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+52x^60+84x^61+111x^62+152x^63+311x^64+138x^65+461x^66+126x^67+632x^68+106x^69+625x^70+112x^71+451x^72+92x^73+258x^74+76x^75+67x^76+64x^77+50x^78+40x^79+17x^80+26x^81+28x^82+6x^83+5x^84+2x^85+2x^86+1x^106

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 1.44 seconds.