The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+68x^68+96x^69+65x^70+116x^71+47x^72+52x^73+20x^74+18x^75+3x^76+8x^78+6x^79+8x^80+2x^82+1x^88+1x^90

The gray image is a code over GF(2) with n=284, k=9 and d=136.
This code was found by Heurico 1.16 in 0.118 seconds.