The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+50x^67+374x^68+546x^69+832x^70+804x^71+1262x^72+1106x^73+1488x^74+1184x^75+1529x^76+1166x^77+1414x^78+946x^79+1082x^80+746x^81+724x^82+370x^83+337x^84+172x^85+132x^86+62x^87+19x^88+6x^89+12x^90+8x^91+4x^92+6x^94+2x^97

The gray image is a code over GF(2) with n=304, k=14 and d=134.
This code was found by Heurico 1.16 in 14 seconds.