The generator matrix

 1  0  1  1  1 X+2  1  1  0 X+2  1  1  1  2  1  1  X  1  1  1  2  1  0  1  1  1  2  2  2  1  1  1  1  1  1  X  X  1  1  1  1 X+2  1  1  1  1  1  1  1  0 X+2  1  1  X X+2  X  1  1  X  X  1  1 X+2  1  1  1  1  X  2  1  1
 0  1  1  0  1  1  X X+3  1  1 X+3 X+2  1  1  0  X  1  3  2 X+1  1 X+2  1 X+1  1  X  1  1  1  0 X+1  X  2 X+2  1  1  1  1  1 X+2 X+2  1 X+3  3 X+3  0 X+3 X+3  3  1  1 X+3  3  1  1  X X+3 X+2  1  0  1  X  1 X+3 X+3  1 X+2  1  1  2  0
 0  0  X  0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  2  0  2  2  2 X+2 X+2 X+2  X X+2 X+2  X X+2  X  X  X  X  X X+2 X+2  2  2  X X+2  0  X  0  0  X  X X+2  2  X  2 X+2  0  X  X  X  2  0  X  0  X  2  0  0 X+2  2 X+2  0  X  0
 0  0  0  X  0  0  X  2  X X+2  X  2 X+2  X  X  2  0  X  0  0 X+2  X  2  X X+2  X  2  X  0 X+2  2  X X+2  0  2  X  X X+2  X  2  2  2  0  X X+2  X  2 X+2 X+2  2  2  X  2  0  0  0  0  0  X  2  X  0  X  2  X  2  X X+2  2  0  0
 0  0  0  0  X  0  0  X  X X+2  2  2  2  2 X+2 X+2  X X+2  X  2  0 X+2  X  0  X X+2  0  X X+2  2 X+2  0 X+2  0  0  2  X  2  X  X X+2  0 X+2 X+2  X  X X+2  0  X  0 X+2  0 X+2 X+2  2  2  2 X+2  0  X  2  2  0  0  X  2  2  2  X  2  0
 0  0  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  2  0  2  0  0  2  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  0  2  2  0  2  0  0  2  2  2  2  0  0  2  2  2  2  2  0  2  0  2  0  2  2  2  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+59x^62+132x^63+213x^64+356x^65+499x^66+568x^67+619x^68+710x^69+708x^70+704x^71+680x^72+652x^73+607x^74+498x^75+413x^76+270x^77+171x^78+110x^79+67x^80+54x^81+30x^82+30x^83+11x^84+4x^85+5x^86+6x^87+10x^88+2x^89+1x^92+1x^94+1x^96

The gray image is a code over GF(2) with n=284, k=13 and d=124.
This code was found by Heurico 1.16 in 5.04 seconds.