The generator matrix

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

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+196x^71+288x^72+402x^73+434x^74+442x^75+426x^76+388x^77+255x^78+232x^79+171x^80+228x^81+145x^82+138x^83+92x^84+80x^85+58x^86+24x^87+36x^88+34x^89+11x^90+8x^91+2x^92+4x^93+1x^94

The gray image is a code over GF(2) with n=308, k=12 and d=142.
This code was found by Heurico 1.16 in 0.949 seconds.