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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+84x^61+136x^62+180x^63+276x^64+310x^65+403x^66+512x^67+500x^68+666x^69+826x^70+720x^71+646x^72+608x^73+602x^74+458x^75+307x^76+274x^77+174x^78+126x^79+116x^80+80x^81+63x^82+46x^83+41x^84+24x^85+4x^86+6x^87+2x^89+1x^104

The gray image is a code over GF(2) with n=284, k=13 and d=122.
This code was found by Heurico 1.16 in 7.11 seconds.