The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+46x^59+330x^60+746x^61+1595x^62+2466x^63+3352x^64+4604x^65+6203x^66+7832x^67+9314x^68+10786x^69+11590x^70+12396x^71+12333x^72+10962x^73+9610x^74+8202x^75+6225x^76+4630x^77+3187x^78+1884x^79+1276x^80+660x^81+413x^82+250x^83+91x^84+54x^85+8x^86+6x^87+6x^88+6x^89+2x^90+6x^91

The gray image is a code over GF(2) with n=284, k=17 and d=118.
This code was found by Heurico 1.13 in 246 seconds.