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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+70x^68+302x^69+606x^70+870x^71+914x^72+1130x^73+1222x^74+1234x^75+1320x^76+1310x^77+1403x^78+1242x^79+1201x^80+982x^81+791x^82+642x^83+354x^84+304x^85+203x^86+126x^87+76x^88+32x^89+31x^90+10x^91+4x^93+2x^95+2x^99

The gray image is a code over GF(2) with n=308, k=14 and d=136.
This code was found by Heurico 1.13 in 5.4 seconds.