The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+142x^71+116x^72+260x^73+88x^74+246x^75+88x^76+266x^77+52x^78+306x^79+72x^80+164x^81+30x^82+90x^83+36x^84+42x^85+14x^86+10x^87+6x^88+4x^89+6x^90+4x^91+2x^95+1x^96+2x^102

The gray image is a code over GF(2) with n=308, k=11 and d=142.
This code was found by Heurico 1.16 in 1.26 seconds.