The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+310x^58+744x^59+1520x^60+1976x^61+3538x^62+4748x^63+6115x^64+7896x^65+9320x^66+10924x^67+11896x^68+12520x^69+11784x^70+11588x^71+9948x^72+8016x^73+6030x^74+4512x^75+3278x^76+1860x^77+1290x^78+552x^79+354x^80+176x^81+100x^82+20x^83+34x^84+4x^85+12x^86+6x^88

The gray image is a code over GF(2) with n=276, k=17 and d=116.
This code was found by Heurico 1.13 in 238 seconds.