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

generates a code of length 61 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+47x^54+8x^55+67x^56+120x^59+512x^61+55x^62+120x^63+36x^64+8x^67+25x^70+21x^72+3x^80+1x^110

The gray image is a code over GF(2) with n=244, k=10 and d=108.
This code was found by Heurico 1.16 in 0.365 seconds.