The generator matrix

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

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+97x^68+408x^69+548x^70+676x^71+898x^72+1324x^73+1085x^74+1340x^75+1256x^76+1386x^77+1286x^78+1376x^79+1105x^80+1064x^81+727x^82+634x^83+389x^84+320x^85+204x^86+122x^87+60x^88+36x^89+19x^90+10x^91+2x^92+6x^93+2x^94+2x^95+1x^98

The gray image is a code over GF(2) with n=308, k=14 and d=136.
This code was found by Heurico 1.16 in 14.2 seconds.