The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+162x^69+163x^70+364x^71+131x^72+550x^73+201x^74+526x^75+98x^76+480x^77+177x^78+522x^79+93x^80+278x^81+105x^82+98x^83+24x^84+52x^85+14x^86+14x^87+12x^89+6x^90+8x^91+2x^92+2x^93+6x^94+4x^95+2x^96+1x^104

The gray image is a code over GF(2) with n=304, k=12 and d=138.
This code was found by Heurico 1.16 in 58.7 seconds.