The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+68x^62+236x^64+28x^65+342x^66+124x^67+453x^68+216x^69+552x^70+280x^71+488x^72+236x^73+334x^74+108x^75+246x^76+32x^77+170x^78+73x^80+60x^82+28x^84+10x^86+10x^88+1x^116

The gray image is a code over GF(2) with n=284, k=12 and d=124.
This code was found by Heurico 1.16 in 1.5 seconds.